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$H$-covering of a supermanifold

Fernando A. Z. Santamaria, Elizaveta Vishnyakova

Abstract

We develop the theory of $H$-graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of $H$-graded coverings of supermanifolds in the case where $H$ is a finite abelian group.

$H$-covering of a supermanifold

Abstract

We develop the theory of -graded manifolds for any finitely generated abelian group, using tools from representation theory. Furthermore, we introduce and investigate the notion of -graded coverings of supermanifolds in the case where is a finite abelian group.
Paper Structure (27 sections, 14 theorems, 113 equations)

This paper contains 27 sections, 14 theorems, 113 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Characters of finite abelian groups
  4. $\operatorname{Ch}(G)$-graded vector superspaces
  5. $\operatorname{Ch}(G)$-decomposition of the sheaf of smooth or holomorphic functions on $V$
  6. Taylor series of homogeneous components
  7. $H$-graded domains
  8. Structure sheaf of a $H$-graded domain
  9. Morphisms of $H$-graded domains
  10. Morphisms of a $H$-graded domain into a superdomain
  11. $H$-graded manifolds
  12. Definition of a $H$-graded manifold
  13. $H$-covering for a superdomain and a supermanifold
  14. $H$-covering of a superdomain
  15. Universal properties of a $H$-covering of a superdomain
  16. ...and 12 more sections

Key Result

Theorem 2

There is the following decomposition

Theorems & Definitions (56)

  • Remark 1
  • Theorem 2
  • proof
  • Remark 3
  • Example 4
  • Remark 5
  • Definition 6
  • Proposition 7
  • proof
  • Remark 8
  • ...and 46 more