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Title: Morse theory, Higgs fields, and Yang-Mills-Higgs functionals
Authors: Bradlow, S.B.
Wilkin, G. 
Keywords: Higgs bundles
Morse theory
surface groups
Issue Date: 2012
Citation: Bradlow, S.B., Wilkin, G. (2012). Morse theory, Higgs fields, and Yang-Mills-Higgs functionals. Journal of Fixed Point Theory and Applications 11 (1) : 1-41. ScholarBank@NUS Repository.
Abstract: In this mostly expository paper we describe applications of Morse theory to moduli spaces of Higgs bundles. The moduli spaces are finite-dimensional analytic varieties but they arise as quotients of infinite-dimensional spaces. There are natural functions for Morse theory on both the infinite-dimensional spaces and the finite-dimensional quotients. The first comes from the Yang-Mills-Higgs energy, while the second is provided by the Hitchin function. After describing what Higgs bundles are, we explore these functions and how they may be used to extract topological information about the moduli spaces. © 2012 Springer Basel AG.
Source Title: Journal of Fixed Point Theory and Applications
ISSN: 16617738
DOI: 10.1007/s11784-012-0073-4
Appears in Collections:Staff Publications

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