A tower connecting gauge groups to string topology
Algebraic Topology
2015-06-19 v3
Abstract
We develop a variant of calculus of functors, and use it to relate the gauge group G(P) of a principal bundle P over M to the Thom ring spectrum (P^Ad)^{-TM}. If P has contractible total space, the resulting Thom ring spectrum is LM^{-TM}, which plays a central role in string topology. R.L. Cohen and J.D.S. Jones have recently observed that, in a certain sense, (P^Ad)^{-TM} is the linear approximation of G(P). We prove an extension of that relationship by demonstrating the existence of higher-order approximations and calculating them explicitly. This also generalizes calculations done by G. Arone.
Cite
@article{arxiv.1209.1778,
title = {A tower connecting gauge groups to string topology},
author = {Cary Malkiewich},
journal= {arXiv preprint arXiv:1209.1778},
year = {2015}
}
Comments
50 pages. Most recent version has a new section on convergence. Accepted for publication in the Journal of Topology