Geometric and topological structures related to M-branes

TL;DR

This paper explores the geometric and topological frameworks underlying M-branes in M-theory, emphasizing structures like String and Fivebrane, and their relation to cohomology, homotopy algebras, and topological modular forms.

Contribution

It provides a comprehensive analysis of the geometric and topological structures associated with M-branes, linking them to advanced cohomology theories and homotopy algebraic structures.

Findings

M2-branes require String structures in spacetime.

M5-branes require Fivebrane structures.

Charges in M-theory relate to Topological Modular forms.

Abstract

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a String structure and a Fivebrane structure, respectively. For the former, we study how the fields in M-theory are associated with the above structures, with homotopy algebras, with twisted cohomology, and with generalized cohomology. We also explain how the corresponding charges should take values in Topological Modular forms. We survey background material and related results in the process.