The topology of moduli spaces of group representations: The case of compact surface

被引：7
|
作者：
Biswas, Indranil [1 ]
Florentino, Carlos [2 ]
机构：
[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India
[2] Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2011年 / 135卷 / 04期
关键词：
Flat connection; Higgs bundle; Representation; PRINCIPAL BUNDLES;
D O I：
10.1016/j.bulsci.2011.02.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a connected complex semisimple affine algebraic group, and let K be a maximal compact subgroup of G. Let X be a noncompact oriented surface. The main theorem of Florentino and Lawton (2009) [3] says that the moduli space of flat K-connections on X is a strong deformation retraction of the moduli space of flat G-connections on X. We prove that this statement fails whenever X is compact of genus at least two. (C) 2011 Elsevier Masson SAS. All rights reserved.
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页码：395 / 399
页数：5
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