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

abstract

  • © 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).

altmetric score

  • 2.6

author list (cited authors)

  • Higson, N., Schick, T., & Xie, Z.

citation count

  • 1

complete list of authors

  • Higson, Nigel||Schick, Thomas||Xie, Zhizhang

publication date

  • September 2018