Consistent Orientation of Moduli Spaces
Abstract
We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is the twisted equivariant K-theory of a compact Lie group. We construct the theory via correspondence diagrams of moduli spaces, which we "linearize" using complex K-theory. A key point in the construction is to consistently orient these moduli spaces to define pushforwards; the consistent orientation induces twistings of complex K-theory. The Madsen-Tillmann spectra play a crucial role.
Cite
@article{arxiv.0711.1909,
title = {Consistent Orientation of Moduli Spaces},
author = {Daniel S. Freed and Michael J. Hopkins and Constantin Teleman},
journal= {arXiv preprint arXiv:0711.1909},
year = {2007}
}
Comments
21 pages, dedicated to Nigel Hitchin on the occasion of his 60th birthday. Version 2 for publication has additional text in section 3 and makes minor corrections