Consistent Orientation of Moduli Spaces

Details Consistent Orientation of Moduli Spaces Consistent Orientation of Moduli Spaces

2007-11-13

arxiv.org/abs/0711.1909v2

Mathematics

Algebraic Topology

21 pages, dedicated to Nigel Hitchin on the occasion of his 60th birthday. Version 2 for publication has additional text in se

Scientific paper

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.

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