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Journal articles on the topic 'Klein bottle'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

SCHELLEKENS, A. N., and N. SOUSA. "OPEN DESCENDANTS OF U(2N) ORBIFOLDS AT RATIONAL RADII." International Journal of Modern Physics A 16, no. 22 (2001): 3659–71. http://dx.doi.org/10.1142/s0217751x01005158.

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We construct explicitly the open descendants of some exceptional automorphism invariants of U (2N) orbifolds. We focus on the case N = p1 × p2, p1 and p2 prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R2 = 2p1/p2. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.

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2

Elitzur, S., and N. Malkin. "Fermionic Klein bottle." Physical Review D 42, no. 4 (1990): 1159–65. http://dx.doi.org/10.1103/physrevd.42.1159.

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3

TERAGAITO, MASAKAZU. "CREATING KLEIN BOTTLES BY SURGERY ON KNOTS." Journal of Knot Theory and Its Ramifications 10, no. 05 (2001): 781–94. http://dx.doi.org/10.1142/s0218216501001153.

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In the present paper, we will study the creation of Klein bottles by Dehn surgery on knots in the 3-sphere, and we will give an upper bound for slopes creating Klein bottles for non-cabled knots by using the genera of knots. In particular, it is shown that if a Klein bottle is created by Dehn surgery on a genus one knot then the knot is a doubled knot. As a corollary, we obtain that genus one, cross-cap number two knots are doubled knot.

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4

Putz, Mihai V., and Ottorino Ori. "Topological Symmetry Transition between Toroidal and Klein Bottle Graphenic Systems." Symmetry 12, no. 8 (2020): 1233. http://dx.doi.org/10.3390/sym12081233.

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In the current study, distance-based topological invariants, namely the Wiener number and the topological roundness index, were computed for graphenic tori and Klein bottles (named toroidal and Klein bottle fullerenes or polyhexes in the pre-graphene literature) described as closed graphs with N vertices and 3N/2 edges, with N depending on the variable length of the cylindrical edge LC of these nano-structures, which have a constant length LM of the Möbius zigzag edge. The presented results show that Klein bottle cubic graphs are topologically indistinguishable from toroidal lattices with the same size (N, LC, LM) over a certain threshold size LC. Both nano-structures share the same values of the topological indices that measure graph compactness and roundness, two key topological properties that largely influence lattice stability. Moreover, this newly conjectured topological similarity between the two kinds of graphs transfers the translation invariance typical of the graphenic tori to the Klein bottle polyhexes with size LC ≥ LC, making these graphs vertex transitive. This means that a traveler jumping on the nodes of these Klein bottle fullerenes is no longer able to distinguish among them by only measuring the chemical distances. This size-induced symmetry transition for Klein bottle cubic graphs represents a relevant topological effect influencing the electronic properties and the theoretical chemical stability of these two families of graphenic nano-systems. The present finding, nonetheless, provides an original argument, with potential future applications, that physical unification theory is possible, starting surprisingly from the nano-chemical topological graphenic space; thus, speculative hypotheses may be drawn, particularly relating to the computational topological unification (that is, complexification) of the quantum many-worlds picture (according to Everett’s theory) with the space-curvature sphericity/roundness of general relativity, as is also currently advocated by Wolfram’s language unification of matter-physical phenomenology.

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5

Maksymenko, Sergiy. "Diffeomorphism groups of Morse-Bott foliation on the solid Klein bottle by Klein bottles parallel to the boundary." Збірник Праць Інституту математики НАН України 20, no. 1 (2023): 896–910. http://dx.doi.org/10.3842/trim.v20n1.532.

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Let $\mathcal{G}$ be a Morse-Bott foliation on the solid Klein bottle $\mathbf{K}$ into $2$-dimensional Klein bottles parallel to the boundary and one singular circle $S^1$. Let also $S^1\widetilde{\times}S^2$ be the twisted bundle over $S^1$ which is a union of two solid Klein bottles $\mathbf{K}_0$ and $\mathbf{K}_1$ with common boundary $K$. Then the above foliation $\mathcal{G}$ on both $\mathbf{K}_0$ and $\mathbf{K}_1$ gives a foliation $\mathcal{G}'$ on $S^1\widetilde{\times}S^2$ into parallel Klein bottles and two singluar circles. The paper computes the homotopy types of groups of foliated (sending leaves to leaves) and leaf preserving diffeomorphisms for foliations $\mathcal{G}$ and $\mathcal{G}'$.

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6

Sabourau, Stéphane, and Zeina Yassine. "Optimal systolic inequalities on Finsler Möbius bands." Journal of Topology and Analysis 08, no. 02 (2016): 349–72. http://dx.doi.org/10.1142/s1793525316500138.

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We prove optimal systolic inequalities on Finsler Möbius bands relating the systole and the height of the Möbius band to its Holmes–Thompson volume. We also establish an optimal systolic inequality for Finsler Klein bottles of revolution, which we conjecture to hold true for arbitrary Finsler metrics. Extremal metric families both on the Möbius band and the Klein bottle are also presented.

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7

Jakobson, Dmitry, Nikolai Nadirashvili, and Iosif Polterovich. "Extremal Metric for the First Eigenvalue on a Klein Bottle." Canadian Journal of Mathematics 58, no. 2 (2006): 381–400. http://dx.doi.org/10.4153/cjm-2006-016-0.

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AbstractThe first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus. We construct an extremal metric on a Klein bottle. It is a metric of revolution, admitting a minimal isometric embedding into a sphere by the first eigenfunctions. Also, this Klein bottle is a bipolar surface for Lawson's -torus. We conjecture that an extremal metric for the first eigenvalue on a Klein bottle is unique, and hence it provides a sharp upper bound for λ1 on a Klein bottle of a given area. We present numerical evidence and prove the first results towards this conjecture.

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8

Lu, Fuliang. "Spanning Trees of Lattices Embedded on the Klein Bottle." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/452453.

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The problem of enumerating spanning trees in lattices with Klein bottle boundary condition is considered here. The exact closed-form expressions of the numbers of spanning trees for 4.8.8 lattice, hexagonal lattice, and 33·42lattice on the Klein bottle are presented.

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9

Davis, Nick. "Inside/Outside the Klein Bottle." Music, Sound, and the Moving Image 6, no. 1 (2012): 9–19. http://dx.doi.org/10.3828/msmi.2012.3.

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10

Davis, Donald M. "An n-dimensional Klein bottle." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 5 (2019): 1207–21. http://dx.doi.org/10.1017/prm.2018.73.

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AbstractAn n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in Euclidean space.

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11

Anderson, John T. "The hull of Rudin’s Klein bottle." Proceedings of the American Mathematical Society 140, no. 2 (2012): 553–60. http://dx.doi.org/10.1090/s0002-9939-2011-10998-5.

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12

Heil, Wolfgang, and Pedja Raspopović. "Dehn fillings of Klein bottle bundles." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (1992): 255–70. http://dx.doi.org/10.1017/s0305004100070948.

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An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

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13

Valdez-Sánchez, Luis G. "Toroidal and Klein bottle boundary slopes." Topology and its Applications 154, no. 3 (2007): 584–603. http://dx.doi.org/10.1016/j.topol.2006.08.001.

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14

Lu, Fuliang, Lianzhu Zhang, and Fenggen Lin. "Dimer statistics on the Klein bottle." Physica A: Statistical Mechanics and its Applications 390, no. 12 (2011): 2315–24. http://dx.doi.org/10.1016/j.physa.2011.02.038.

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15

Wang, Yan. "Pfaffian polyominos on the Klein bottle." Journal of Mathematical Chemistry 56, no. 10 (2018): 3147–60. http://dx.doi.org/10.1007/s10910-018-0938-x.

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16

Bača, Martin, Maria Naseem, and Ayesha Shabbir. "Face labelings of Klein-bottle fullerenes." Acta Mathematicae Applicatae Sinica, English Series 33, no. 2 (2017): 277–86. http://dx.doi.org/10.1007/s10255-017-0658-1.

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17

Hidber, Cristhian E., and Miguel A. Xicoténcatl. "Characteristic classes of Klein bottle bundles." Topology and its Applications 220 (April 2017): 1–13. http://dx.doi.org/10.1016/j.topol.2017.01.026.

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18

Cohen, Daniel C., and Lucile Vandembroucq. "Topological complexity of the Klein bottle." Journal of Applied and Computational Topology 1, no. 2 (2017): 199–213. http://dx.doi.org/10.1007/s41468-017-0002-0.

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19

Schrijver, A. "The Klein bottle and multicommodity flows." Combinatorica 9, no. 4 (1989): 375–84. http://dx.doi.org/10.1007/bf02125349.

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20

Zhaoxiang, Li, and Liu Yanpei. "Singular maps on the Klein bottle." Applied Mathematics-A Journal of Chinese Universities 17, no. 3 (2002): 365–70. http://dx.doi.org/10.1007/s11766-002-0016-8.

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21

Lawrencenko, Serge, and Seiya Negami. "Irreducible Triangulations of the Klein Bottle." Journal of Combinatorial Theory, Series B 70, no. 2 (1997): 265–91. http://dx.doi.org/10.1006/jctb.1997.9999.

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22

Cheshkova, M. A. "Deformation of one-sided surfaces." Differential Geometry of Manifolds of Figures, no. 52 (2021): 114–51. http://dx.doi.org/10.5922/0321-4796-2020-52-14.

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The work is devoted to the study of the deformation of one-sided surfaces. Let a normal vector be drawn along a closed curve on the surface. If, when returning to the original point, the direction of the normal coincides with the original direction of the normal, then the surface is called two-sided. Otherwise, we have a one-sided surface. Unilateral surfaces include: crossed cap, Roman surface, Boya surface, Klein bottle. Roman surface, Boya surface and crossed hood are a model of the projective plane. It is proved that if the surface is a model of a Moebius strip, of a Klein bottle, of projective plane, then the surface deformation is a Moebius strip model, a Klein bottle model, projective plane model respectively. Using a mathematical package, graphs are built the surfaces under consideration.

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23

Torriani, Hugo H. "Profinite completions of the fundamental group of the Klein bottle." Czechoslovak Mathematical Journal 35, no. 4 (1985): 511–14. http://dx.doi.org/10.21136/cmj.1985.102044.

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24

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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25

Šuch, Ondrej. "Vertex transitive maps on the Klein bottle." Ars Mathematica Contemporanea 4, no. 2 (2011): 363–74. http://dx.doi.org/10.26493/1855-3974.133.bf8.

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26

Franzoni, Gregorio. "The Klein Bottle: Variations on a Theme." Notices of the American Mathematical Society 59, no. 08 (2012): 1076. http://dx.doi.org/10.1090/noti880.

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27

Jiang, Cuipo, Jingjing Jiang, and Yufeng Pei. "The q-Analog Klein Bottle Lie Algebra." Algebra Colloquium 21, no. 04 (2014): 561–74. http://dx.doi.org/10.1142/s1005386714000510.

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In this paper, we study an infinite-dimensional Lie algebra ℬq, called the q-analog Klein bottle Lie algebra. We show that ℬq is a finitely generated simple Lie algebra with a unique (up to scalars) symmetric invariant bilinear form. The derivation algebra and the universal central extension of ℬq are also determined.

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28

El Mir, Chady, and Zeina Yassine. "Conformal geometric inequalities on the Klein bottle." Conformal Geometry and Dynamics of the American Mathematical Society 19, no. 11 (2015): 240–57. http://dx.doi.org/10.1090/ecgd/283.

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29

Matveev, S. V., and L. R. Nabeeva. "Tabulating knots in the thickened Klein bottle." Siberian Mathematical Journal 57, no. 3 (2016): 542–48. http://dx.doi.org/10.1134/s0037446616030174.

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30

Séquin, Carlo H. "On the number of Klein bottle types." Journal of Mathematics and the Arts 7, no. 2 (2013): 51–63. http://dx.doi.org/10.1080/17513472.2013.795883.

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31

Nemirovski, Stefan Yu. "Homology class of a Lagrangian Klein bottle." Izvestiya: Mathematics 73, no. 4 (2009): 689–98. http://dx.doi.org/10.1070/im2009v073n04abeh002462.

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32

Kawarabayashi, Ken-ichi, Daniel Král', Jan Kynčl, and Bernard Lidický. "6-Critical Graphs on the Klein Bottle." SIAM Journal on Discrete Mathematics 23, no. 1 (2009): 372–83. http://dx.doi.org/10.1137/070706835.

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33

Cortés, C., and A. Nakamoto. "Diagonal flips in outer-Klein-bottle triangulations." Discrete Mathematics 222, no. 1-3 (2000): 41–50. http://dx.doi.org/10.1016/s0012-365x(00)00004-2.

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34

Beaudou, Laurent, Antoine Gerbaud, Roland Grappe, and Frédéric Palesi. "Drawing Disconnected Graphs on the Klein Bottle." Graphs and Combinatorics 26, no. 4 (2010): 471–81. http://dx.doi.org/10.1007/s00373-010-0928-7.

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35

Král’, Daniel, Bojan Mohar, Atsuhiro Nakamoto, Ondřej Pangrác, and Yusuke Suzuki. "Coloring Eulerian Triangulations of the Klein Bottle." Graphs and Combinatorics 28, no. 4 (2011): 499–530. http://dx.doi.org/10.1007/s00373-011-1063-9.

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36

Asayama, Yoshihiro, Naoki Matsumoto, Atsuhiro Nakamoto, and Shota Ogano. "Generating Even Triangulations on the Klein Bottle." Graphs and Combinatorics 34, no. 4 (2018): 727–57. http://dx.doi.org/10.1007/s00373-018-1909-5.

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37

Lambe, Larry A. "An algebraic study of the Klein Bottle." Journal of Homotopy and Related Structures 11, no. 4 (2016): 885–91. http://dx.doi.org/10.1007/s40062-016-0156-9.

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38

Raspopović, Pedja. "Incompressible surfaces in punctured Klein bottle bundles." Topology and its Applications 49, no. 2 (1993): 95–113. http://dx.doi.org/10.1016/0166-8641(93)90037-e.

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39

Swindale, Nicholas V. "Visual cortex: Looking into a Klein bottle." Current Biology 6, no. 7 (1996): 776–79. http://dx.doi.org/10.1016/s0960-9822(02)00592-4.

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40

Anosov, D. V. "ON INFINITE CURVES ON THE KLEIN BOTTLE." Mathematics of the USSR-Sbornik 66, no. 1 (1990): 41–58. http://dx.doi.org/10.1070/sm1990v066n01abeh002080.

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41

El-Ahmady, A. E. "On Elastic Klein Bottle and Fundamental Groups." Applied Mathematics 04, no. 03 (2013): 499–504. http://dx.doi.org/10.4236/am.2013.43074.

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42

Ichihara, Kazuhiro, and Masakazu Teragaito. "Klein bottle surgery and genera of knots." Pacific Journal of Mathematics 210, no. 2 (2003): 317–33. http://dx.doi.org/10.2140/pjm.2003.210.317.

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43

Louko, Jorma. "Witten's 2 + 1 gravity on (Klein bottle)." Classical and Quantum Gravity 12, no. 10 (1995): 2441–67. http://dx.doi.org/10.1088/0264-9381/12/10/006.

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44

Anderson, John T., Purvi Gupta, and Edgar L. Stout. "The rational hull of Rudin’s Klein bottle." Proceedings of the American Mathematical Society 147, no. 9 (2019): 3859–66. http://dx.doi.org/10.1090/proc/14514.

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45

Chenette, Nathan, Luke Postle, Noah Streib, et al. "Six-Critical Graphs on the Klein Bottle." Electronic Notes in Discrete Mathematics 31 (August 2008): 235–40. http://dx.doi.org/10.1016/j.endm.2008.06.047.

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46

Chenette, Nathan, Luke Postle, Noah Streib, Robin Thomas, and Carl Yerger. "Five-coloring graphs on the Klein bottle." Journal of Combinatorial Theory, Series B 102, no. 5 (2012): 1067–98. http://dx.doi.org/10.1016/j.jctb.2012.05.001.

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47

Ren, Han, and Yanpei Liu. "4-Regular Maps on the Klein Bottle." Journal of Combinatorial Theory, Series B 82, no. 1 (2001): 118–37. http://dx.doi.org/10.1006/jctb.2000.2030.

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48

N. A. Koam, Ali, Ali Ahmad, Maryam Salem Alatawi, Muhammad Azeem, and Muhammad Faisal Nadeem. "Metric Basis of Four-Dimensional Klein Bottle." Computer Modeling in Engineering & Sciences 136, no. 3 (2023): 3011–24. http://dx.doi.org/10.32604/cmes.2023.024764.

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49

Tiwari, Anand K., Amit Tripathi, Yogendra Singh, and Punam Gupta. "Doubly Semiequivelar Maps on Torus and Klein Bottle." Journal of Mathematics 2020 (March 24, 2020): 1–14. http://dx.doi.org/10.1155/2020/5674172.

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A tiling of the Euclidean plane, by regular polygons, is called 2-uniform tiling if it has two orbits of vertices under the action of its symmetry group. There are 20 distinct 2-uniform tilings of the plane. Plane being the universal cover of torus and Klein bottle, it is natural to ask about the exploration of maps on these two surfaces corresponding to the 2-uniform tilings. We call such maps as doubly semiequivelar maps. In the present study, we compute and classify (up to isomorphism) doubly semiequivelar maps on torus and Klein bottle. This classification of semiequivelar maps is useful in classifying a category of symmetrical maps which have two orbits of vertices, named as 2-uniform maps.

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50

López, Gabriel. "Accumulation points of flows on the Klein bottle." Discrete and Continuous Dynamical Systems 9, no. 2 (2002): 497–503. http://dx.doi.org/10.3934/dcds.2003.9.497.

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