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International Journal of Theoretical Physics

, Volume 39, Issue 5, pp 1221–1231 | Cite as

Supersmooth Topoi

  • Hirokazu Nishimura
Article

Abstract

It is well known that supersmooth functions are more akin to holomorphicfunctions than to smooth functions. The ultimate object of study in complexgeometry is not merely complex manifolds, but complex spaces, in whichholomorphic functions may be nilpotent and consequently invisible from ageometric viewpoint. Supergeometers have long been searching for an appropriatedefinition of supermanifold, for which many classical results in the theory ofsmooth manifolds can naturally be superized. However, they have not proceededfurther in quest of a supersmooth equivalent of complex space. The principalobject of this paper is to introduce the notion of supersmooth superspace intosupergeometry after the classical definition of complex space in complexgeometry, and then to build a good model of synthetic supergeometry after themanner of Dubuc and Taubin (1983), thereby superseding Yetter (1988). Themodel to be constructed is a Grothendieck topos encompassing the category ofG-supermanifolds and G-mappings as a full subcategory.

Keywords

Manifold Field Theory Elementary Particle Quantum Field Theory Topo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Hirokazu Nishimura
    • 1
  1. 1.Institute of MathematicsUniversity of Tsukuba, TsukubaIbarakiJapan

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