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Type: Journal article
Title: Bundle gerbes and moduli spaces
Author: Bouwknegt, P.
Varghese, M.
Wu, S.
Citation: Journal of Geometry and Physics, 2012; 62(1):1-10
Publisher: Elsevier Science BV
Issue Date: 2012
ISSN: 0393-0440
Statement of
Peter Bouwknegt, Varghese Mathai and Siye Wu
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.
Keywords: Index bundle grebe
Caloron bundle grebe
Moduli spaces
Rights: © 2011 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.geomphys.2011.08.005
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