Obstructions, Extensions and Reductions. Some applications of Cohomology

TL;DR

This paper explores how cohomology classes serve as obstructions to certain geometric structures and discusses their applications in physics, particularly in reduced holonomy within M- and F-theory.

Contribution

It introduces cohomology obstructions to orientation and spin structures and applies these concepts to problems in theoretical physics involving reduced holonomy.

Findings

Cohomology classes act as obstructions to geometric structures.

Applications to reduced holonomy in M- and F-theory.

Insights into physical implications of cohomological obstructions.

Abstract

After introducing some cohomology classes as obstructions to orientation and spin structures etc., we explain some applications of cohomology to physical problems, in special to reduced holonomy in M- and F-theory.