Elliptic Operators and Higher Signatures

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.