On Carvalho's $K$-theoretic formulation of the cobordism invariance of the index

Details On Carvalho's $K$-theoretic formulation of the cobordism invariance of the index On Carvalho's $K$-theoretic formulation of the cobordism invariance of the index

2006-12-08

arxiv.org/abs/math/0612217v1

Proc. Amer. Mat. Soc. 134 (2006), 3395-3404

Mathematics

Analysis of PDEs

10 pages

Scientific paper

We give an analytic proof of the fact that the index of an elliptic operator
on the boundary of a compact manifold vanishes when the principal symbol comes
from the restriction of a $K$-theory class from the interior. The proof uses
noncommutative residues inside the calculus of cusp pseudodifferential
operators of Melrose.

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