C∗–algebraic higher signatures and an invariance theorem in codimension two

© 2018, Mathematical Sciences Publishers. All rights reserved. We revisit the construction of signature classes in C*–algebra K–theory, and develop a variation that allows us to prove equality of signature classes in some situations involving homotopy equivalences of noncompact manifolds that are only defined outside a compact set. As an application, we prove a counterpart for signature classes of a codimension-two vanishing theorem for the index of the Dirac operator on spin manifolds (the latter is due to Hanke, Pape and Schick, and is a development of well-known work of Gromov and Lawson).

C∗–algebraic higher signatures and an invariance theorem in codimension two Academic Article