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Synthetic Theory of Superconnections

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Abstract

In our preceding two papers we have developed synthetic differentialsupergeometry up to the basic theory of differential forms. In this paper we givethe notion of connection, as well as its accompanying notions of connection formand curvature form, superized in our synthetic context, and establish the secondBianchi identity synthetically.

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REFERENCES

  • Bartocci, C., Bruzzo, U., and Hernández-Ruipérez, D. (1991).The Geometry of Supermanifolds, Kluwer, Dordrecht. DeWitt, B. (1984).Supermanifolds, Cambridge University Press, Cambridge.

    Google Scholar 

  • Kock, A. (1981).Synthetic Differential Geometry, Cambridge University Press, Cambridge.

    Google Scholar 

  • Kock, A. (1996). Combinatorics of curvature and the Bianchi identity,Theory and Applications of Categories 2, 69-89.

    Google Scholar 

  • Lavendhomme, R. (1996).Basic Concepts of Synthetic Differential Geometry, Kluwer, Dordrecht.

    Google Scholar 

  • Manin, Y. I. (1988).Gauge Field Theory and Complex Geometry, Springer, Berlin and Heidelberg.

    Google Scholar 

  • Moerdijk, I., and Reyes, G. E. (1991).Models for Smooth Infinitesimal Analysis, Springer-Verlag, New York.

    Google Scholar 

  • Nishimura, H. (1998). Synthetic differential supergeometry,International Journal of Theoretical Physics,37, 2803-2822.

    Google Scholar 

  • Nishimura, H. (1999). Differential forms in synthetic differential supergeometry,International Journal of Theoretical Physics,38, 653-663.

    Google Scholar 

  • Nishimura, H. (2000). Another curvature in synthetic differential geometry,Bulletin Belgian Mathematical Society, to appear.

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Nishimura, H. Synthetic Theory of Superconnections. International Journal of Theoretical Physics 39, 297–320 (2000). https://doi.org/10.1023/A:1003632208750

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  • DOI: https://doi.org/10.1023/A:1003632208750

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