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Connected Components of The Space of Surface Group Representations | | Nan-Kuo Ho
; Chiu-Chu Melissa Liu
; | | Date: |
20 Mar 2003 | | Journal: | IMRN 2003, no.44, 2359-2372 | | Subject: | Symplectic Geometry; Differential Geometry MSC-class: 53D99 | math.SG math.DG | | Abstract: | Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $Sigma$ of genus $l >1$, the order of the group $H^2(Sigma,pi_1(G))$ is equal to the number of connected components of the space $Hom(pi_1(Sigma),G)/G$ which can also be identified with the moduli space of gauge equivalence classes of flat G-bundles over $Sigma$. We show that the same statement for a closed compact nonorientable surface which is homeomorphic to the connected sum of k copies of the real projective plane, where $k
eq 1,2,4$, can be easily derived from a result in A. Alekseev, A.Malkin and E. Meinrenken’s recent work on Lie group valued moment maps. | | Source: | arXiv, math.SG/0303255 | | Services: | Forum | Review | PDF | Favorites | |
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