Relative Chern character, boundaries and index formulae
Differential Geometry
2010-12-30 v2 K-Theory and Homology
Abstract
For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have `geometric K-theory', namely the `transmission algebra' introduced by Boutet de Monvel, the `zero algebra' introduced by Mazzeo and the `scattering algebra' from [MR95k:58168] we give explicit formulae for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fibre operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of a vector bundle over a manifold with boundary in which the Chern character, mapping from the corresponding realization of K-theory, naturally takes values.
Keywords
Cite
@article{arxiv.0808.0183,
title = {Relative Chern character, boundaries and index formulae},
author = {Pierre Albin and Richard Melrose},
journal= {arXiv preprint arXiv:0808.0183},
year = {2010}
}