Superconnections and Index Theory
Differential Geometry
2011-05-03 v2 K-Theory and Homology
Abstract
We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities.
Keywords
Cite
@article{arxiv.0810.0820,
title = {Superconnections and Index Theory},
author = {Alexander Kahle},
journal= {arXiv preprint arXiv:0810.0820},
year = {2011}
}
Comments
29 pages, 1 figure; minor updates and corrections; final version