Topology of character varieties of Abelian groups

Autor:	Florentino, C., Lawton, S.
Rok vydání:	2013
Předmět:	Mathematics - Algebraic Geometry Mathematics - Geometric Topology Mathematics - Representation Theory Primary 14L30 14P25 Secondary 14L17 14L24 22E46
Zdroj:	Topology and its Applications, Volume 173, 15 August 2014, Pages 32-58
Druh dokumentu:	Working Paper
DOI:	10.1016/j.topol.2014.05.009
Popis:	Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the conjugation orbit space Hom(A,K)/K is a strong deformation retract of the GIT quotient space Hom(A,G)//G. As a corollary, we determine necessary and sufficient conditions for the character variety Hom(A,G)//G to be irreducible when G is connected and semisimple. For a general connected reductive G, analogous conditions are found to be sufficient for irreducibility, when A is free abelian. Comment: 33 pages; version 3: few small changes, one error corrected, one or two additional references; to appear in Topology and its Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1301.7616 Zobrazit plný text záznamu View this record from Arxiv