Twisting cochains and higher torsion
Algebraic Topology
2011-07-05 v3 K-Theory and Homology
Abstract
This paper gives a short summary of the central role played by Ed Brown's "twisting cochains" in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisting cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR torsion. Flat superconnections are also equivalent to twisting cochains.
Keywords
Cite
@article{arxiv.math/0212383,
title = {Twisting cochains and higher torsion},
author = {Kiyoshi Igusa},
journal= {arXiv preprint arXiv:math/0212383},
year = {2011}
}
Comments
23 pages, 1 figure, dedicated to Edgar Brown. Revised following suggestions by referee