Abstract
Super line bundles over supermanifolds are introduced as natural generalizations of line bundles over smooth manifolds. Their classification in terms of their obstruction class and the representation of their Chern class in terms of a connection on the super line bundle are discussed. The case where the base supermanifold is De Witt is analyzed in detail, both in the supersmooth and complex superanalytic case.
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References
Bartocci, C. and Bruzzo, U., J. Geom. Phys. 4, 391 (1987); Bartocci, C., Bruzzo, U., and Hernández Ruipérez, D., A remark on a new category of supermanifolds, Preprint Dipartimento di Matematica, Univ di Genova (1988).
Friedan, D., in D. Gross and M. Green (eds.), Proceedings of the Workshop on Unified String Theories, World Scientific, Singapore, 1986; Giddings, S. B. and Nelson, P., Phys. Rev. Lett. 59, 2619 (1987); Commun. Math. Phys. 118, 289 (1988); Hodgkin, L., Problems of fields on super Riemann surfaces, King's College Preprint, London (1988).
Rogers, A., J. Math. Phys. 21, 1352 (1980).
Rogers, A., Commun. Math. Phys. 105, 375 (1986).
Bruzzo, U., in K. Bleuler and M. Werner (eds.), Proceedings of the XVIth International Conference on Differential Geometric Methods in Theoretical Physics, Kluwer, Dordrecht, 1988.
Rothstein, M., Trans. Amer. Math. Soc. 287, 159 (1986).
Rabin, J. M., Commun. Math. Phys. 108, 375 (1987).
Bartocci, C. and Bruzzo, U., J. Math. Phys. 28, 2363 (1987).
Bartocci, C. and Bruzzo, U., J. Math. Phys. 29, 1789 (1988).
Bartocci, C., Bruzzo, U., and Landi, G., Chern-Simons forms on principal super fibre bundles, Preprint S.I.S.S.A. 109/87/FM, Trieste (1987).
Godement, R., Théorie des faisceaux, Hermann, Paris, 1964.
Hoyos, J., Quirós, M., Ramírez Mittelbrunn, J., and de Urríes, F. J., J. Math. Phys. 25, 847 (1984).
Hirzebruch, F., Topological Methods in Algebraic Geometry, Springer-Verlag, Berlin, 1966.
Bartocci, C. and Bruzzo, U., On De Witt supermanifolds and their Picard variety, Preprint Dipartimento di Matematica, Univ. di Genova (1989).
Atiyah, M. F., Trans. Amer. Math. Soc. 85, 181–207 (1957).
Bartocci, C. and Bruzzo, U., Existence of connections on superbundles, Lett. Math. Phys. 17, 61 (1989).