Bundle gerbes and moduli spaces

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2012

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Bouwknegt, P.
Varghese, M.
Wu, S.

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Journal of Geometry and Physics, 2012; 62(1):1-10

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Peter Bouwknegt, Varghese Mathai and Siye Wu

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Abstract

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces. © 2011 Elsevier B.V.

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© 2011 Elsevier B.V. All rights reserved.

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