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. 
Eric Leichtnam and Paolo Piazza