Do there exist some relations between Functional Analysis and Algebraic Topology? As the title: does there exist some relations between Functional Analysis and Algebraic Topology.
As we have known, the tools developed in Algebraic Topology are used to classify spaces, especially the geometrical structures in finite dimensional Euclidean space. But when we come across some infinite dimensional spaces, such as Banach spaces, do the tools in Algebraic Topology also take effect?
Moreover, are there some books discussing such relation? My learning background is listed following:basic algebra(group, ring, field, polynomial); Rudin's real & complex analysis and functional analysis; general topology(Munkres level).
Any viewpoint will be appreciated.

See Atiyah–Singer index theorem:
http://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem.
