Pure and Applied Mathematics Quarterly
Volume 12 (2016)
$K$-homology and Fredholm operators II: elliptic operators
Pages: 225 – 241
We give a simple and direct proof of the Atiyah–Singer–Kasparov theorem in $K$-homology, which reduces the full theorem for elliptic operators to the special case of Dirac operators. This is done by proving commutativity of a triangle of abelian groups.
elliptic operator, Dirac operator, $K$-homology, Thom isomorphism, Atiyah–Singer index theorem
The first author was partially supported by NSF grant DMS-0701184.
The second author was partially supported by NSF grant DMS-1100570.
Received 20 November 2016
Published 9 February 2018