Consistent Orientation of Moduli Spaces

Daniel S. Freed; Michael J. Hopkins; Constantin Teleman

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arXiv · 0711.1909

Consistent Orientation of Moduli Spaces

Daniel S. Freed·Michael J. Hopkins·Constantin Teleman

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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.

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BibTeX RIS

Daniel S. Freed, Michael J. Hopkins, Constantin Teleman. 2007-12-19. Consistent Orientation of Moduli Spaces. https://arxiv.org/abs/0711.1909

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