Infinite-dimensional supermanifolds over arbitrary base fields

Forum Mathematicum

Volumn 24, Issue 3, 2012, Pages 565-608

  Alldridge, Alexander ^a   Laubinger, Martin ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b UNIVERSITY OF PADERBORN   (Germany)

Author keywords

functor of points; Infinite dimensional supermanifold

Indexed keywords

EID: 84861510989     PISSN: 09337741     EISSN: 14355337     Source Type: Journal    
DOI: 10.1515/form.2011.074     Document Type: Article

References (26)

1. F. A. Berezin, Introduction to Superanalysis, Mathematical Physics and Applied Mathematics 9, D. Reidel Publishing Co., Dordrecht, 1987.
2. W. Bertram, H. Glöckner and K.-H. Neeb, Differential calculus over general base fields and rings, Expo. Math. 22 (2004), no. 3, 213-282.
3. N. Bourbaki, General Topology. Chapters 1-4, Elements of Mathematics, Springer- Verlag, Berlin, 1989.
4. P. Deligne and J.W. Morgan, Notes on supersymmetry (following Joseph Bernstein), in: Quantum Fields and Strings: A Course for Mathematicians, Volume 1, pp. 41-97, American Mathematical Society, Providence, RI, 1999.
5. B. S. DeWitt, Supermanifolds, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984.
6. R. Fioresi, M. A. Lledó, and V. S. Varadarajan, The Minkowski and conformal superspaces, J. Math. Phys. 48 (2007), no. 11.
7. H. Glöckner, R. Gramlich and T. Hartnick, Final group topologies, Kac-Moody groups, and Pontryagin duality, Israel J. Math. 177 (2010), 49-102.
8. J. Giraud, Cohomologie non abélienne, Grundlehren der mathematischen Wissenschaften 179, Springer-Verlag, Berlin, 1971.
9. A. Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. 4 (1960), 5-228.
10. Z. Jaskólski, Smooth coalgebras, J. Geom. Phys. 29 (1999), no. 1-2, 87-150.
11. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, in: Differential Geometrical Methods in Mathematical Physics, pp. 177-306, Lecture Notes in Mathematics 570, Springer-Verlag, Berlin, 1977.
12. D. Leites, Introduction to the theory of supermanifolds, Russian Math. Surveys 35 (1980), no. 1, 1-64.
13. Y. I. Manin, Gauge Field Theory and Complex Geometry, Grundlehren der Mathematischen Wissenschaften 289, Springer-Verlag, Berlin, 1988.
14. D. S. Metzler, Topological and smooth stacks, arXiv:math/0306176v1, 2003.
15. V. Molotkov, Infinite-dimensional Zk2 -manifolds, ICTP preprints IC/84/183, 1984.
16. C. Sachse, Global analytic approach to super Teichmüller spaces, PhD thesis, Universität Leipzig, 2007.
17. C. Sachse, A categorical formulation of superalgebra and supergeometry, preprint, arXiv:0802.4067, 2008.
18. C. Sachse and C. Wockel, The diffeomorphism supergroup of a finite-dimensional supermanifold, arXiv:0904.2726v2 [math.DG], 2009.
19. T. Schmitt, Super differential geometry, Akademie der Wissenschaften der DDR, Institut für Mathematik, Report R-MATH-05/84, 1984.
20. T. Schmitt, Infinite-dimensional supermanifolds I, Akademie derWissenschaften der DDR, Institut für Mathematik, Report R-MATH-88-08, 1988.
21. A. S. Schwarz, On the definition of superspace, Theoret. Math. Phys. 60 (1984), no. 1, 657-660.
22. G. M. Tuynman, Functions of class Ck without derivatives, Publ. Mat. 41 (1997), no. 2, 417-435.
23. G. M. Tuynman, Supermanifolds and Supergroups. Basic Theory, Mathematics and its Applications 570, Kluwer Academic Publishers, Dordrecht, 2004.
24. A. Vistoli, Grothendieck topologies, fibered categories and descent theory, in: Fundamental Algebraic Geometry, pp. 1-104, Mathematical Surveys and Monographs 123, American Mathematical Society, Providence, RI, 2005.
25. A. A. Voronov, Mappings of supermanifolds, Theoret. Math. Phys. 60 (1984), no. 1, 660-664.
26. A. Yamasaki, Inductive limit of general linear groups, J. Math. Kyoto Univ. 38 (1998), no. 4, 769-779.