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Journal articles on the topic 'Supergeometry'

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Published: 4 June 2021
Last updated: 10 March 2023

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1

Goertsches, O. "Riemannian supergeometry." Mathematische Zeitschrift 260, no. 3 (December 9, 2007): 557–93. http://dx.doi.org/10.1007/s00209-007-0288-z.

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2

Tsimpis, Dimitrios. "Curved 11D Supergeometry." Journal of High Energy Physics 2004, no. 11 (December 2, 2004): 087. http://dx.doi.org/10.1088/1126-6708/2004/11/087.

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3

Fioresi, R., and F. Zanchetta. "Representability in supergeometry." Expositiones Mathematicae 35, no. 3 (September 2017): 315–25. http://dx.doi.org/10.1016/j.exmath.2016.10.001.

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4

CATTANEO, ALBERTO S., and FLORIAN SCHÄTZ. "INTRODUCTION TO SUPERGEOMETRY." Reviews in Mathematical Physics 23, no. 06 (July 2011): 669–90. http://dx.doi.org/10.1142/s0129055x11004400.

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These notes are based on a series of lectures given by the first author at the school of "Poisson 2010", held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.
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5

Voronov, A. A., Yu I. Manin, and I. B. Penkov. "Elements of supergeometry." Journal of Soviet Mathematics 51, no. 1 (August 1990): 2069–83. http://dx.doi.org/10.1007/bf01098184.

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6

Schwarz, A., and I. Shapiro. "Supergeometry and arithmetic geometry." Nuclear Physics B 756, no. 3 (November 2006): 207–18. http://dx.doi.org/10.1016/j.nuclphysb.2006.08.024.

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7

Hoker, E. D., and D. H. Phong. "Complex geometry and supergeometry." Current Developments in Mathematics 2005, no. 1 (2005): 1–40. http://dx.doi.org/10.4310/cdm.2005.v2005.n1.a1.

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8

Lott, John. "Torsion constraints in supergeometry." Communications in Mathematical Physics 133, no. 3 (November 1990): 563–615. http://dx.doi.org/10.1007/bf02097010.

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9

Schmitt, Thomas. "Supergeometry and hermitian conjugation." Journal of Geometry and Physics 7, no. 2 (January 1990): 141–69. http://dx.doi.org/10.1016/0393-0440(90)90009-r.

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10

Schwarz, Albert. "Noncommutative supergeometry, duality and deformations." Nuclear Physics B 650, no. 3 (February 2003): 475–96. http://dx.doi.org/10.1016/s0550-3213(02)01088-x.

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11

Noja, Simone. "Supergeometry of Π-projective spaces." Journal of Geometry and Physics 124 (January 2018): 286–99. http://dx.doi.org/10.1016/j.geomphys.2017.11.010.

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12

Grabowski, Janusz, David Khudaverdyan, and Norbert Poncin. "The supergeometry of Loday algebroids." Journal of Geometric Mechanics 5, no. 2 (2013): 185–213. http://dx.doi.org/10.3934/jgm.2013.5.185.

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13

de Goursac, Axel. "Noncommutative supergeometry and quantum supergroups." Journal of Physics: Conference Series 597 (April 13, 2015): 012028. http://dx.doi.org/10.1088/1742-6596/597/1/012028.

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14

Howe, P. S., and G. Papadopoulos. "N=2, d=2 supergeometry." Classical and Quantum Gravity 4, no. 1 (January 1, 1987): 11–21. http://dx.doi.org/10.1088/0264-9381/4/1/005.

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15

Bruzzo, Ugo, and Vladimir Pestov. "On the notion of compactness in supergeometry." Bulletin of the Australian Mathematical Society 61, no. 3 (June 2000): 473–88. http://dx.doi.org/10.1017/s0004972700022504.

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We discuss the problem of finding an analogue of the concept of topological space in supergeometry, motivated by the search for a procedure to compactify supermanifolds along odd coordinates. In particular, we examine the topologies arising naturally on the sets of points of locally ringed superspaces, and show that in the presence of a nontrivial odd sector such topologies are never compact. The main outcome of our discussion is the following new observation: not only the usual framework of supergeometry (the theory of locally ringed spaces), but the more general approach of the functor of points, need to be further enlarged.
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16

Kuzenko, Sergei M., and Gabriele Tartaglino-Mazzucchelli. "Conformally flat supergeometry in five dimensions." Journal of High Energy Physics 2008, no. 06 (June 27, 2008): 097. http://dx.doi.org/10.1088/1126-6708/2008/06/097.

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17

Steif, Alan R. "Supergeometry of three-dimensional black holes." Physical Review D 53, no. 10 (May 15, 1996): 5521–26. http://dx.doi.org/10.1103/physrevd.53.5521.

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18

Manin, Yu I. "Holomorphic supergeometry and Yang-Mills superfields." Journal of Soviet Mathematics 30, no. 2 (July 1985): 1927–75. http://dx.doi.org/10.1007/bf02105859.

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19

Catenacci, Roberto, Pietro Antonio Grassi, and Simone Noja. "Superstring field theory, superforms and supergeometry." Journal of Geometry and Physics 148 (February 2020): 103559. http://dx.doi.org/10.1016/j.geomphys.2019.103559.

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20

Hack, Thomas-Paul, Florian Hanisch, and Alexander Schenkel. "Supergeometry in Locally Covariant Quantum Field Theory." Communications in Mathematical Physics 342, no. 2 (December 1, 2015): 615–73. http://dx.doi.org/10.1007/s00220-015-2516-4.

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21

Awada, M. A. "Non-commutative supergeometry and superstring field theory." Nuclear Physics B 281, no. 1-2 (January 1987): 145–56. http://dx.doi.org/10.1016/0550-3213(87)90251-3.

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22

VARSAIE, S. "ON A THEORY OF CHERN CLASSES FOR SUPER VECTOR BUNDLES." International Journal of Geometric Methods in Modern Physics 05, no. 03 (May 2008): 287–95. http://dx.doi.org/10.1142/s0219887808002771.

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In this paper, a theory of characteristic classes for super vector bundles over [Formula: see text] is studied. Some properties of even and odd Chern classes, constructed in this theory, are established. At last, the relevance of the theory to supergeometry is discussed.
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23

PLETNIOV, N. G. "GENERALIZED CONFORMAL FLAT D 10 N 1 SUPERGEOMETRY." International Journal of Modern Physics A 06, no. 26 (November 10, 1991): 4667–80. http://dx.doi.org/10.1142/s0217751x91002203.

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D 10 N 1 supergeometry of flat superspace conformal deformations is considered on the phase of a spontaneous breakdown of the OSp(32/1) supergroup. The correspondence between the standard set of constraints and the field equations of D 10 N 1 pure supergravity and the linear approximation of nonlinear realizations of OSp(32/1) in vielbein and superconnection definitions is demonstrated.
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24

Schomerus, Volker, and Hubert Saleur. "The WZW-model: From supergeometry to logarithmic CFT." Nuclear Physics B 734, no. 3 (February 2006): 221–45. http://dx.doi.org/10.1016/j.nuclphysb.2005.11.013.

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25

Jia, Bei. "Topological string theory revisited I: The stage." International Journal of Modern Physics A 31, no. 24 (August 30, 2016): 1650135. http://dx.doi.org/10.1142/s0217751x16501359.

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In this paper, we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten (Superstring perturbation theory revisited, arXiv:1209.5461 ). We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.
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26

Noja, Simone. "Non-Projected Supermanifolds and Embeddings in Super Grassmannians." Universe 4, no. 11 (November 5, 2018): 114. http://dx.doi.org/10.3390/universe4110114.

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In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results (L. Sergio et al., 2018), we study an explicit example of non-projected and non-projective supermanifold over the projective plane and show how to embed it into a super Grassmannian. The geometry of super Grassmannians is also reviewed in detail.
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27

Cremonini, C. A., and P. A. Grassi. "Self-dual forms in supergeometry I: The chiral boson." Nuclear Physics B 973 (December 2021): 115596. http://dx.doi.org/10.1016/j.nuclphysb.2021.115596.

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28

Alekseevsky, D. V., V. Cortés, C. Devchand, and U. Semmelmann. "Killing spinors are killing vector fields in Riemannian supergeometry." Journal of Geometry and Physics 26, no. 1-2 (June 1998): 37–50. http://dx.doi.org/10.1016/s0393-0440(97)00036-3.

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29

Gates, S. J., P. S. Howe, and C. M. Hull. "Quantum supersymmetry and the supergeometry of four-dimensional superstrings." Physics Letters B 227, no. 1 (August 1989): 49–54. http://dx.doi.org/10.1016/0370-2693(89)91282-3.

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30

Chung, Won Sang. "Purely cubic action for superstring field via noncommutative supergeometry." International Journal of Theoretical Physics 33, no. 3 (March 1994): 593–97. http://dx.doi.org/10.1007/bf00670518.

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31

Bruzzo, Ugo, Daniel Hernández Ruipérez, and Alexander Polishchuk. "Notes on fundamental algebraic supergeometry. Hilbert and Picard superschemes." Advances in Mathematics 415 (February 2023): 108890. http://dx.doi.org/10.1016/j.aim.2023.108890.

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32

Hasebe, Kazuki, and Keisuke Totsuka. "Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry." Symmetry 5, no. 2 (April 26, 2013): 119–214. http://dx.doi.org/10.3390/sym5020119.

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33

Arbuzov, Andrej B., and Diego Julio Cirilo-Lombardo. "Dynamical breaking of symmetries beyond the standard model and supergeometry." Physica Scripta 94, no. 12 (September 26, 2019): 125302. http://dx.doi.org/10.1088/1402-4896/ab35f6.

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34

Castro, Carlos. "Super-Clifford Gravity, Higher Spins, Generalized Supergeometry and Much More." Advances in Applied Clifford Algebras 24, no. 1 (December 4, 2013): 55–69. http://dx.doi.org/10.1007/s00006-013-0433-1.

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35

Pestov, Vladimir G. "Analysis on superspace: an overview." Bulletin of the Australian Mathematical Society 50, no. 1 (August 1994): 135–65. http://dx.doi.org/10.1017/s0004972700009643.

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The concept of superspace is fundamental for some recent physical theories, notably supersymmetry, and a mathematical feedback for it is provided by superanalysis and supergeometry. We survey the state of affairs in superanalysis, shifting our attention from supermanifold theory to “plain” superspaces. The two principal existing approaches to superspaces are sketched and links between them discussed. We examine a problem by Manin of representing even geometry (analysis) as a collective effect in infinite-dimensional purely odd geometry (analysis), by applying the technique of nonstandard (infinitesimal) analysis.
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36

Schmitt, T. "Supergeometry and Quantum Field Theory, or: What is a Classical Configuration?" Reviews in Mathematical Physics 09, no. 08 (November 1997): 993–1052. http://dx.doi.org/10.1142/s0129055x97000348.

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We discuss the conceptual difficulties connected with the anticommutativity of classical fermion fields, and we argue that the "space" of all classical configurations of a model with such fields should be described as an infinite-dimensional supermanifold M. We discuss the two main approaches to supermanifolds, and we examine the reasons why many physicists tend to prefer the Rogers approach although the Berezin–Kostant–Leites approach is the more fundamental one. We develop the infinite-dimensional variant of the latter, and we show that the superfunctionals considered in [44] are nothing but superfunctions on M. We propose a programme for future mathematical work, which applies to any classical field model with fermion fields. A part of this programme will be implemented in the successor paper [45].
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37

Macdowell, Samuel W., and Mark T. Rakowski. "Supergeometry of the coupled Yang-Mills/supergravity system in ten dimensions." Nuclear Physics B 274, no. 3-4 (September 1986): 589–99. http://dx.doi.org/10.1016/0550-3213(86)90528-6.

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38

Kruglikov, Boris, Andrea Santi, and Dennis The. "G(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equation." Advances in Mathematics 376 (January 2021): 107420. http://dx.doi.org/10.1016/j.aim.2020.107420.

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39

de Beer, Willem, André van Tonder, and João P. Rodrigues. "Superinvolutions on super-Riemann surfaces and the supergeometry of type-I superstrings." Physics Letters B 248, no. 1-2 (September 1990): 67–72. http://dx.doi.org/10.1016/0370-2693(90)90016-y.

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40

Zhang, De-Hai. "Tensor analysis on conformal supergeometry and the ghost action of the superstring." Physics Letters B 196, no. 3 (October 1987): 321–24. http://dx.doi.org/10.1016/0370-2693(87)90740-4.

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41

Bruce, Andrew James, and Janusz Grabowski. "Riemannian Structures on Z 2 n -Manifolds." Mathematics 8, no. 9 (September 1, 2020): 1469. http://dx.doi.org/10.3390/math8091469.

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Very loosely, Z2n-manifolds are ‘manifolds’ with Z2n-graded coordinates and their sign rule is determined by the scalar product of their Z2n-degrees. A little more carefully, such objects can be understood within a sheaf-theoretical framework, just as supermanifolds can, but with subtle differences. In this paper, we examine the notion of a Riemannian Z2n-manifold, i.e., a Z2n-manifold equipped with a Riemannian metric that may carry non-zero Z2n-degree. We show that the basic notions and tenets of Riemannian geometry directly generalize to the setting of Z2n-geometry. For example, the Fundamental Theorem holds in this higher graded setting. We point out the similarities and differences with Riemannian supergeometry.
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42

GATES, S. JAMES, and J. W. DURACHTA. "GAUGE TWO-FORM IN D=4, N=4 SUPERGEOMETRY WITH SU(4) SUPERSYMMETRY." Modern Physics Letters A 04, no. 21 (October 20, 1989): 2007–16. http://dx.doi.org/10.1142/s0217732389002264.

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We employ a gauge two-form [Formula: see text] in place of the pseudoscalar B' to produce a version of on-shell D=4, N=4 superspace supergravity with SU(4) symmetry. The replacement is accomplished using the Chern-Simons forms associated with the six spin-1 fields of N=4 supergravity. Finally, a Green-Schwarz action is presented and the relation of the theory to the N=4, D=4 heterotic string is exhibited.
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43

de Goursac, Axel, and Jean-Philippe Michel. "Superunitary Representations of Heisenberg Supergroups." International Mathematics Research Notices 2020, no. 19 (August 14, 2018): 5926–6006. http://dx.doi.org/10.1093/imrn/rny184.

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Abstract Numerous Lie supergroups do not admit superunitary representations (SURs) except the trivial one, for example, Heisenberg and orthosymplectic supergroups in mixed signature. To avoid this situation, we introduce in this paper a broader definition of SUR, relying on a new definition of Hilbert superspace. The latter is inspired by the notion of Krein space and was developed initially for noncommutative supergeometry. For Heisenberg supergroups, this new approach yields a smooth generalization, whatever the signature, of the unitary representation theory of the classical Heisenberg group. First, we obtain Schrödinger-like representations by quantizing generic coadjoint orbits. They satisfy the new definition of irreducible SURs and serve as ground to the main result of this paper: a generalized Stone–von Neumann theorem. Then, we obtain the superunitary dual and build a group Fourier transformation, satisfying Parseval theorem. We eventually show that metaplectic representations, which extend Schrödinger-like representations to metaplectic supergroups, also fit into this definition of SURs.
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44

BARRON, KATRINA. "THE MODULI SPACE OF N = 2 SUPER-RIEMANN SPHERES WITH TUBES." Communications in Contemporary Mathematics 09, no. 06 (December 2007): 857–940. http://dx.doi.org/10.1142/s0219199707002666.

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Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N = 2 superconformal field theory, we define the moduli space of N = 2 super-Riemann spheres with oriented and ordered half-infinite tubes (or equivalently, oriented and ordered punctures, and local superconformal coordinates vanishing at the punctures), modulo N = 2 superconformal equivalence. We develop a formal theory of infinitesimal N = 2 superconformal transformations based on a representation of the N = 2 Neveu–Schwarz algebra in terms of superderivations. In particular, via these infinitesimals we present the Lie supergroup of N = 2 superprojective transformations of the N = 2 super-Riemann sphere. We give a reformulation of the moduli space in terms of these infinitesimals. We introduce generalized N = 2 super-Riemann spheres with tubes and discuss some group structures associated to certain moduli spaces of both generalized and non-generalized N = 2 super-Riemann spheres. We define an action of the symmetric groups on the moduli space. Lastly we discuss the nonhomogeneous (versus homogeneous) coordinate system associated to N = 2 superconformal structures and the corresponding results in this coordinate system.
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45

Ikeda, Noriaki, and Xiaomeng Xu. "Canonical functions, differential graded symplectic pairs in supergeometry, and Alexandrov-Kontsevich-Schwartz-Zaboronsky sigma models with boundaries." Journal of Mathematical Physics 55, no. 11 (November 2014): 113505. http://dx.doi.org/10.1063/1.4900834.

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46

Antunes, Paulo, and Camille Laurent-Gengoux. "Jacobi structures in supergeometric formalism." Journal of Geometry and Physics 61, no. 11 (November 2011): 2254–66. http://dx.doi.org/10.1016/j.geomphys.2011.06.001.

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47

VARSAIE, S. "ν-CLASSES." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250028. http://dx.doi.org/10.1142/s0219887812500284.

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ν-classes are supergeometric generalization of the Chern classes. Associated to each superline bundle over supermanifold [Formula: see text], ν-class is an element of the second cohomology group of M with coefficients in ℤ[ν] with ν2 = 1.
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48

GRABOWSKI, JANUSZ. "BRACKETS." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360001. http://dx.doi.org/10.1142/s0219887813600013.

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We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as in the supergeometric setting. The review is supplemented by some new concepts and examples.
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49

Cattaneo, A. S., and M. Zambon. "A Supergeometric Approach to Poisson Reduction." Communications in Mathematical Physics 318, no. 3 (February 10, 2013): 675–716. http://dx.doi.org/10.1007/s00220-013-1664-7.

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50

VARSAIE, S. "ν-SPHERES, ν-DEGREES AND ν-ALGEBRAS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (November 2009): 1089–95. http://dx.doi.org/10.1142/s0219887809004090.

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A novel supergeometric generalization of common n-sphere, called ν-sphere, is introduced. It is shown that a canonical volume form exists on a ν-sphere. Then a concept of degree is developed for the maps between them. Finally, a semigroup action on ν-spheres is discussed.
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