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Artykuły w czasopismach na temat „Surfaces non orientables”

Autor: Grafiati

Data publikacji: 19 października 2024

Data aktualizacji: 31 lipca 2025

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1

Oliveira, M. Elisa G. G., and Eric Toubiana. "Surfaces non-orientables de genre deux." Boletim da Sociedade Brasileira de Matem�tica 24, no. 1 (1993): 63–88. http://dx.doi.org/10.1007/bf01231696.

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2

Toubiana, E. "Surfaces minimales non orientables de genre quelconque." Bulletin de la Société mathématique de France 121, no. 2 (1993): 183–95. http://dx.doi.org/10.24033/bsmf.2206.

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3

Bhowmik, Debashis, Dipendu Maity, and Eduardo Brandani Da Silva. "Surface codes and color codes associated with non-orientable surfaces." Quantum Information and Computation 21, no. 13&14 (2021): 1135–53. http://dx.doi.org/10.26421/qic21.13-14-4.

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Silva et al. produced quantum codes related to topology and coloring, which are associated with tessellations on the orientable surfaces of genus $\ge 1$ and the non-orientable surfaces of the genus 1. Current work presents an approach to build quantum surface and color codes} on non-orientable surfaces of genus $ \geq 2n+1 $ for $n\geq 1$. We also present several tables of new surface and color codes related to non-orientable surfaces. These codes have the ratios $k/n$ and $d/n$ better than the codes obtained from orientable surfaces.

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4

NAKAMURA, GOU. "COMPACT NON-ORIENTABLE SURFACES OF GENUS 5 WITH EXTREMAL METRIC DISCS." Glasgow Mathematical Journal 54, no. 2 (2011): 273–81. http://dx.doi.org/10.1017/s0017089511000589.

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AbstractA compact hyperbolic surface of genus g is called an extremal surface if it admits an extremal disc, a disc of the largest radius determined by g. Our problem is to find how many extremal discs are embedded in non-orientable extremal surfaces. It is known that non-orientable extremal surfaces of genus g > 6 contain exactly one extremal disc and that of genus 3 or 4 contain at most two. In the present paper we shall give all the non-orientable extremal surfaces of genus 5, and find the locations of all extremal discs in those surfaces. As a consequence, non-orientable extremal surfac

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5

Yurttaş, S. Öykü. "Curves on Non-Orientable Surfaces and Crosscap Transpositions." Mathematics 10, no. 9 (2022): 1476. http://dx.doi.org/10.3390/math10091476.

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Let Ng,n be a non-orientable surface of genus g with n punctures and one boundary component. In this paper, we describe multicurves in Ng,n making use of generalized Dynnikov coordinates, and give explicit formulae for the action of crosscap transpositions and their inverses on the set of multicurves in Ng,n in terms of generalized Dynnikov coordinates. This provides a way to solve on non-orientable surfaces various dynamical and combinatorial problems that arise in the study of mapping class groups and Thurston’s theory of surface homeomorphisms, which were solved only on orientable surfaces

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6

Sabloff, Joshua. "On a refinement of the non-orientable 4-genus of Torus knots." Proceedings of the American Mathematical Society, Series B 10, no. 22 (2023): 242–51. http://dx.doi.org/10.1090/bproc/166.

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In formulating a non-orientable analogue of the Milnor Conjecture on the 4 4 -genus of torus knots, Batson [Math. Res. Lett. 21 (2014), pp. 423–436] developed an elegant construction that produces a smooth non-orientable spanning surface in B 4 B^4 for a given torus knot in S 3 S^3 . While Lobb [Math. Res. Lett. 26 (2019), pp. 1789] showed that Batson’s surfaces do not always minimize the non-orientable 4 4 -genus, we prove that they do minimize among surfaces that share their normal Euler number. We also determine the possible pairs of normal Euler number and first Betti number for non-orient

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7

Gastesi, Pablo Arés. "Some results on Teichmüller spaces of Klein surfaces." Glasgow Mathematical Journal 39, no. 1 (1997): 65–76. http://dx.doi.org/10.1017/s001708950003192x.

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The deformation theory of nonorientable surfaces deals with the problem of studying parameter spaces for the different dianalytic structures that a surface can have. It is an extension of the classical theory of Teichmüller spaces of Riemann surfaces, and as such, it is quite rich. In this paper we study some basic properties of the Teichmüller spaces of non-orientable surfaces, whose parallels in the orientable situation are well known. More precisely, we prove an uniformization theorem, similar to the case of Riemann surfaces, which shows that a non-orientable compact surface can be represen

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8

Nowik, Tahl. "Immersions of non-orientable surfaces." Topology and its Applications 154, no. 9 (2007): 1881–93. http://dx.doi.org/10.1016/j.topol.2007.02.007.

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9

Maloney, Alexander, and Simon F. Ross. "Holography on non-orientable surfaces." Classical and Quantum Gravity 33, no. 18 (2016): 185006. http://dx.doi.org/10.1088/0264-9381/33/18/185006.

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10

Goulden, Ian P., Jin Ho Kwak, and Jaeun Lee. "Enumerating branched orientable surface coverings over a non-orientable surface." Discrete Mathematics 303, no. 1-3 (2005): 42–55. http://dx.doi.org/10.1016/j.disc.2003.10.030.

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11

Singerman, David. "Orientable and non-orientable Klein surfaces with maximal symmetry." Glasgow Mathematical Journal 26, no. 1 (1985): 31–34. http://dx.doi.org/10.1017/s0017089500005747.

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Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a

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12

Kamada, Seiichi. "Orientable surfaces in the 4-sphere associated with non-orientable knotted surfaces." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 2 (1990): 299–306. http://dx.doi.org/10.1017/s0305004100069152.

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Let F be a closed connected and non-orientable surface smoothly embedded in the 4-sphere S4 with normal Euler number e(F) = 0. We note that if e(F) = 0, then the non-orientable genus n is even (ef. [7]) and the tubular neighbourhood N(F) of F in S4 which is a D2-bundle over F has a trivial I-subbundle. Let τ be a trivial I-subbundle of N(F) and let τ* = F × I ⊂ N(F) be its orthogonal I-subbundle which is twisted. Then is a closed connected genus n – 1 orientable surface smoothly embedded in S4 and doubly covers F. We call this surface a doubled surface of F in S4 (associated with τ). If a triv

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13

Zwart, Gysbert. "Matrix theory on non-orientable surfaces." Physics Letters B 429, no. 1-2 (1998): 27–34. http://dx.doi.org/10.1016/s0370-2693(98)00420-1.

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14

Cámpora, Daniel, Jaime de la Torre, Juan Carlos García Vázquez, and Fernando Sancho Caparrini. "BML model on non-orientable surfaces." Physica A: Statistical Mechanics and its Applications 389, no. 16 (2010): 3290–98. http://dx.doi.org/10.1016/j.physa.2010.03.037.

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15

Matignon, D., and N. Sayari. "Non-Orientable Surfaces and Dehn Surgeries." Canadian Journal of Mathematics 56, no. 5 (2004): 1022–33. http://dx.doi.org/10.4153/cjm-2004-046-9.

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AbstractLet K be a knot in S3. This paper is devoted to Dehn surgeries which create 3-manifolds containing a closed non-orientable surface . We look at the slope p/q of the surgery, the Euler characteristic χ() of the surface and the intersection number s between and the core of the Dehn surgery. We prove that if χ() ≥ 15 – 3q, then s = 1. Furthermore, if s = 1 then q ≤ 4 – 3χ() or K is cabled and q ≤ 8 – 5χ(). As consequence, if K is hyperbolic and χ() = –1, then q ≤ 7.

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16

Balacheff, Florent, and Daniel Massart. "Stable norms of non-orientable surfaces." Annales de l’institut Fourier 58, no. 4 (2008): 1337–69. http://dx.doi.org/10.5802/aif.2386.

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17

Etayo Gordejuela, J. J. "Non-orientable automorphisms of Riemann surfaces." Archiv der Mathematik 45, no. 4 (1985): 374–84. http://dx.doi.org/10.1007/bf01198242.

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18

Conder, Marston, and Brent Everitt. "Regular maps on non-orientable surfaces." Geometriae Dedicata 56, no. 2 (1995): 209–19. http://dx.doi.org/10.1007/bf01267644.

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19

End, Werner. "Non-orientable surfaces in 3-manifolds." Archiv der Mathematik 59, no. 2 (1992): 173–85. http://dx.doi.org/10.1007/bf01190680.

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20

PULCINI, GABRIELE. "Rewriting systems for the surface classification theorem." Mathematical Structures in Computer Science 20, no. 4 (2010): 577–88. http://dx.doi.org/10.1017/s0960129510000101.

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The work reported in this paper refers to Massey's proof of the surface classification theorem based on the standard word-rewriting treatment of surfaces. We arrange this approach into a formal rewriting systemand provide a new version of Massey's argument. Moreover, we study the computational properties of two subsystems of:orfor dealing with words denoting orientable surfaces andnorfor dealing with words denoting non-orientable surfaces. We show how such properties induce an alternative proof for the surface classification in which the basic homeomorphism between the connected sum of three p

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21

Abbott, Steve, David M. Jackson, and Terry I. Visentin. "An Atlas of Smaller Maps in Orientable and Non-Orientable Surfaces." Mathematical Gazette 85, no. 504 (2001): 573. http://dx.doi.org/10.2307/3621828.

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22

MA, XIANG, та PENG WANG. "COMPLETE STATIONARY SURFACES IN ${\mathbb R}^4_1$ WITH TOTAL GAUSSIAN CURVATURE – ∫ KdM = 4π". International Journal of Mathematics 24, № 11 (2013): 1350088. http://dx.doi.org/10.1142/s0129167x13500882.

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We classify complete, algebraic, spacelike stationary (i.e. zero mean curvature) surfaces in four-dimensional Lorentz space [Formula: see text] with total Gaussian curvature – ∫ K d M = 4π. Such surfaces must be orientable surfaces, congruent to either the generalized catenoids or the generalized Enneper surfaces. The least total Gaussian curvature of a non-orientable algebraic stationary surface is 6π, which can be realized by Meeks' Möbius strip and its deformations (and also by a new class of non-algebraic examples). When the genus of its oriented double covering [Formula: see text] is g, w

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23

Mitchell, Jane M. O. "The Genus of the Coxeter Graph." Canadian Mathematical Bulletin 38, no. 4 (1995): 462–64. http://dx.doi.org/10.4153/cmb-1995-067-7.

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AbstractIn [1], Biggs stated that the Coxeter graph can be embedded in an orientable surface of genus 3. The purpose of this note is to point out that Biggs' embedding is in fact into a non-orientable surface. Further, it is shown that the orientable genus is 3 and the non-orientable genus is 6.

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24

Bae, Yongju, J. Scott Carter, Seonmi Choi, and Sera Kim. "Non-orientable surfaces in 4-dimensional space." Journal of Knot Theory and Its Ramifications 23, no. 11 (2014): 1430002. http://dx.doi.org/10.1142/s021821651430002x.

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This paper is a survey paper that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their 3-dimensional projections, and indeed the illustrations here depend upon a further projection into the plane of the page. The concepts used to develop the illustrations will be developed herein.

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25

Iwakura, Miwa, and Chuichiro Hayashi. "Non-orientable fundamental surfaces in lens spaces." Topology and its Applications 156, no. 10 (2009): 1753–66. http://dx.doi.org/10.1016/j.topol.2009.03.002.

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26

Bernardi, Olivier, and Guillaume Chapuy. "Counting unicellular maps on non-orientable surfaces." Advances in Applied Mathematics 47, no. 2 (2011): 259–75. http://dx.doi.org/10.1016/j.aam.2010.09.001.

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27

Dranishnikov, Alexander. "On topological complexity of non-orientable surfaces." Topology and its Applications 232 (December 2017): 61–69. http://dx.doi.org/10.1016/j.topol.2017.09.022.

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28

Qiu, Weiyang. "Non-orientable Lagrangian Surfaces with Controlled Area." Mathematical Research Letters 8, no. 6 (2001): 693–701. http://dx.doi.org/10.4310/mrl.2001.v8.n6.a1.

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29

Cimasoni, David. "Dimers on Graphs in Non-Orientable Surfaces." Letters in Mathematical Physics 87, no. 1-2 (2009): 149–79. http://dx.doi.org/10.1007/s11005-009-0299-2.

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30

Burton, Benjamin A., Arnaud de Mesmay, and Uli Wagner. "Finding Non-orientable Surfaces in 3-Manifolds." Discrete & Computational Geometry 58, no. 4 (2017): 871–88. http://dx.doi.org/10.1007/s00454-017-9900-0.

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31

Dupont, Grégoire, and Frédéric Palesi. "Quasi-cluster algebras from non-orientable surfaces." Journal of Algebraic Combinatorics 42, no. 2 (2015): 429–72. http://dx.doi.org/10.1007/s10801-015-0586-1.

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32

Tesler, Glenn. "Matchings in Graphs on Non-orientable Surfaces." Journal of Combinatorial Theory, Series B 78, no. 2 (2000): 198–231. http://dx.doi.org/10.1006/jctb.1999.1941.

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33

Teragaito, Masakazu. "On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces." Canadian Mathematical Bulletin 49, no. 4 (2006): 624–27. http://dx.doi.org/10.4153/cmb-2006-057-5.

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AbstractFor a non-trivial knot in the 3-sphere, only integral Dehn surgery can create a closed 3-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.

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34

Costa, Antonio F., Milagros Izquierdo, and Ana Maria Porto. "On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary." International Journal of Mathematics 28, no. 05 (2017): 1750038. http://dx.doi.org/10.1142/s0129167x17500380.

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In this work, we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus [Formula: see text] with one boundary component is connected and in the case of non-orientable Klein surfaces it has [Formula: see text] components, if [Formula: see text] is odd, and [Formula: see text] components for even [Formula: see text]. We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.

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35

Sidorov, Sergey V., and Ekaterina E. Chilina. "On non-hyperbolic algebraic automorphisms of a two-dimensional torus." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 3 (2021): 295–307. http://dx.doi.org/10.15507/2079-6900.23.202103.295-307.

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Abstract. This paper contains a complete classification of algebraic non-hyperbolic automorphisms of a two-dimensional torus, announced by S. Batterson in 1979. Such automorphisms include all periodic automorphisms. Their classification is directly related to the topological classification of gradient-like diffeomorphisms of surfaces, since according to the results of V. Z. Grines and A.N. Bezdenezhykh, any gradient like orientation-preserving diffeomorphism of an orientable surface is represented as a superposition of the time-1 map of a gradient-like flow and some periodic homeomorphism. J.

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36

COSTA, ANTONIO F., WENDY HALL, and DAVID SINGERMAN. "DOUBLES OF KLEIN SURFACES." Glasgow Mathematical Journal 54, no. 3 (2012): 507–15. http://dx.doi.org/10.1017/s0017089512000109.

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Historical note. A non-orientable surface of genus 2 (meaning 2 cross-caps) is popularly known as the Klein bottle. However, the term Klein surface comes from Felix Klein's book “On Riemann's Theory of Algebraic Functions and their Integrals” (1882) where he introduced such surfaces in the final chapter.

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37

Johnson, F. E. A. "A class of non-Kählerian manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 3 (1986): 519–21. http://dx.doi.org/10.1017/s030500410006624x.

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Let S+ (resp. S−) denote the class of fundamental groups of closed orientable (resp. non-orientable) 2-manifolds of genus ≥ 2, and let surface = S+ ∪ S−. In the list of problems raised at the 1977 Durham Conference on Homological Group Theory occurs the following([7], p. 391, (G. 3)).

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38

WOOD, JOHN C. "HARMONIC MORPHISMS AND HERMITIAN STRUCTURES ON EINSTEIN 4-MANIFOLDS." International Journal of Mathematics 03, no. 03 (1992): 415–39. http://dx.doi.org/10.1142/s0129167x92000187.

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We show that a submersive harmonic morphism from an orientable Einstein 4-manifold M4 to a Riemann surface, or a conformal foliation of M4 by minimal surfaces, determines an (integrable) Hermitian structure with respect to which it is holomorphic. Conversely, any nowhere-Kähler Hermitian structure of an orientable anti-self-dual Einstein 4-manifold arises locally in this way. In the case M4=ℝ4 we show that a Hermitian structure, viewed as a map into S2, is a harmonic morphism; in this case and for S4, [Formula: see text] we determine all (submersive) harmonic morphisms to surfaces locally, and

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39

Antolín, Yago, Warren Dicks, and Peter A. Linnell. "Non-orientable surface-plus-one-relation groups." Journal of Algebra 326, no. 1 (2011): 4–33. http://dx.doi.org/10.1016/j.jalgebra.2009.03.001.

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40

Auckly, David, and Rustam Sadykov. "On non‐orientable surfaces embedded in 4‐manifolds." Journal of Topology 14, no. 2 (2021): 587–607. http://dx.doi.org/10.1112/topo.12188.

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41

VENDRÚSCOLO, D. "BOUNDS ON COINCIDENCE INDICES ON NON-ORIENTABLE SURFACES." Chinese Annals of Mathematics 26, no. 02 (2005): 315–22. http://dx.doi.org/10.1142/s0252959905000257.

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42

Gadgil, Siddhartha, and Dishant Pancholi. "Homeomorphisms and the homology of non-orientable surfaces." Proceedings Mathematical Sciences 115, no. 3 (2005): 251–57. http://dx.doi.org/10.1007/bf02829656.

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43

Norbury, Paul. "Lengths of geodesics on non-orientable hyperbolic surfaces." Geometriae Dedicata 134, no. 1 (2008): 153–76. http://dx.doi.org/10.1007/s10711-008-9251-3.

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44

Bujalance, E., J. M. Gamboa, and C. Maclachlan. "Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism." Glasgow Mathematical Journal 37, no. 2 (1995): 221–32. http://dx.doi.org/10.1017/s0017089500031128.

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In the nineteenth century, Hurwitz [8] and Wiman [14] obtained bounds for the order of the automorphism group and the order of each automorphism of an orientable and unbordered compact Klein surface (i. e., a compact Riemann surface) of topological genus g s 2. The corresponding results of bordered surfaces are due to May, [11], [12]. These may be considered as particular cases of the general problem of finding the minimum topological genus of a surface for which a given finite group G is a group of automorphisms. This problem was solved for cyclic and abelian G by Harvey [7] and Maclachlan [1

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45

Tarkaev, V. V. "AN ANALOGUE OF TURAEV COMULTIPLICATION FOR KNOTS IN NON-ORIENTABLE THICKENING OF A NON-ORIENTABLE SURFACE." Челябинский физико-математический журнал 10, no. 1 (2025): 112–25. https://doi.org/10.47475/2500-0101-2025-10-1-112-125.

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46

GRIGGS, TERRY S., CONSTANTINOS PSOMAS, and JOZEF ŠIRÁŇ. "MAXIMUM GENUS EMBEDDINGS OF LATIN SQUARES." Glasgow Mathematical Journal 60, no. 2 (2017): 495–504. http://dx.doi.org/10.1017/s0017089517000234.

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AbstractIt is proved that every non-trivial Latin square has an upper embedding in a non-orientable surface and every Latin square of odd order has an upper embedding in an orientable surface. In the latter case, detailed results about the possible automorphisms and their actions are also obtained.

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47

Szepietowski, Błażej. "Mapping class group of a non-orientable surface and moduli space of Klein surfaces." Comptes Rendus Mathematique 335, no. 12 (2002): 1053–56. http://dx.doi.org/10.1016/s1631-073x(02)02617-1.

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48

Fine, Benjamin, and Gerhard Rosenberger. "Surface groups within Baumslag doubles." Proceedings of the Edinburgh Mathematical Society 54, no. 1 (2011): 91–97. http://dx.doi.org/10.1017/s0013091509001102.

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AbstractA conjecture of Gromov states that a one-ended word-hyperbolic group must contain a subgroup that is isomorphic to the fundamental group of a closed hyperbolic surface. Recent papers by Gordon and Wilton and by Kim and Wilton give sufficient conditions for hyperbolic surface groups to be embedded in a hyperbolic Baumslag double G. Using Nielsen cancellation methods based on techniques from previous work by the second author, we prove that a hyperbolic orientable surface group of genus 2 is embedded in a hyperbolic Baumslag double if and only if the amalgamated word W is a commutator: t

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49

Satoh, Shin. "Triple point invariants of non-orientable surface-links." Topology and its Applications 121, no. 1-2 (2002): 207–18. http://dx.doi.org/10.1016/s0166-8641(01)00118-3.

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50

Kuno, Erika. "Uniform hyperbolicity for curve graphs of non-orientable surfaces." Hiroshima Mathematical Journal 46, no. 3 (2016): 343–55. http://dx.doi.org/10.32917/hmj/1487991626.

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