Elliptic Operators and Higher Signatures

Abstract

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.

54 pages. Survey-article. Related papers can be retrieved from http://www.mat.uniroma1.it/people/piazza