higherindex
Higherindex is a term used primarily in mathematics to describe a family of invariants that generalize the analytic index of elliptic operators by incorporating group actions and noncommutative geometry. In its most developed form, the Mishchenko–Fomenko higher index promotes the index of an elliptic operator on a closed manifold to a K-theory class in the C*-algebra of the manifold’s fundamental group.
Construction typically begins with a closed manifold M and its universal cover \tilde M, which carries an
Applications of higher indices include obstructions to positive scalar curvature, rigidity phenomena in geometry, and connections
History and development center on the work of Mishchenko and Fomenko in the 1960s–70s, with significant later