A classical approach to smooth supermanifolds

TL;DR

This thesis reinterprets differential supergeometry using classical differential geometry to avoid problematic odd coordinates and facilitate explicit calculations, bridging abstract theory with practical tools.

Contribution

It provides a classical differential geometric framework for supermanifolds, avoiding local odd coordinates and enabling more explicit calculations.

Findings

Reformulation of supergeometry in classical terms

Avoidance of local odd coordinates

Enhanced tools for explicit calculations

Abstract

This is the author's Master's thesis written under the supervision of Dr. Gregor Weingart at the National Autonomous University of Mexico. The purpose of this study is to rewrite differential supergeometry in terms of classical differential geometry. This rewriting from "first principles" has two main motivations: 1 avoid using local (and usually not very well-defined) odd coordinates; 2 use both the language and the tools (both highly-developed) of classical differential geometry to state and prove results in supergeometry. Although there is work in this direction this work's point of view might be useful to translate from the sheaf-theoretic language to one that is better suited for explicit calculations.