Linear Z₂ⁿ-Manifolds and Linear Actions

2020/11/30 by Andrew James Bruce, Eduardo Ibarguengoytia, Eduardo Ibarguëngoytia +1
Mathematics · Physics and Astronomy · #Combinatorics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #math-ph #math.AG #math.DG #math.MP #msc:14A22 #msc:14L30 #msc:58A50 #msc:58C50

paper · pdf · doi:10.3842/sigma.2021.060

published as SIGMA 17 (2021), 060, 58 pages

arxiv created 2021/06/16 · openalex publication_date 2021/06/16 · arxiv updated 2021/06/17 · openalex created_date 2021/06/22 · openalex updated_date 2026/08/05

Abstract

We establish the representability of the general linear Z n 2 -group and use the restricted functor of points -whose test category is the category of Z n 2 -manifolds over a single topological point -to define its smooth linear actions on Z n 2 -graded vector spaces and linear Z n 2 -manifolds. Throughout the paper, particular emphasis is placed on the full faithfulness and target category of the restricted functor of points of a number of categories that we are using.

Citations

• Topological Vector Spaces and Algebras
• The inverse function theorem of Nash and Moser
• The Frobenius theorem for ℤⁿ₂-supermanifolds
• Differential calculus on ℤⁿ₂-supermanifolds
• Homotopical algebraic context over differential operators
• Categories for the Working Mathematician
• Algebraic Geometry