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arXiv · 1209.1778

A tower connecting gauge groups to string topology

Cary Malkiewich
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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.

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Cary Malkiewich. 2015-02-06. A tower connecting gauge groups to string topology. https://doi.org/10.1112/jtopol%2Fjtv003

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