  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.

Differential Geometry;High Energy Physics - Theory;Algebraic Topology