New methods for old spaces: synthetic differential geometry

TL;DR

This paper surveys aspects of synthetic differential geometry, emphasizing the neighbor relation as a fundamental concept, and discusses innovative methods applied to classical geometric spaces.

Contribution

It introduces new methods within synthetic differential geometry focusing on the neighbor relation as a core notion.

Findings

Highlights the importance of neighbor relations in differential geometry

Provides new approaches to classical geometric spaces

Synthesizes existing concepts with novel methods

Abstract

Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.