Elliptic Operators and Higher Signatures

2004/06/01 by Leichtnam, Eric, Piazza, Paolo
#19K56 #58J20 #58J22 #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0406020

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.

Related

• Simple homotopy invariance of higher signatures
• On the homotopy invariance of higher signatures for manifolds with boundary
• Signatures and Higher Signatures of S¹-Quotients
• On the cut and paste property of higher signatures of a closed oriented manifold
• G-Homotopy Invariance of the Analytic Signature of Proper Co-compact G-manifolds and Equivariant Novikov Conjecture