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COHOMOLOGY OF SL(2, C) CHARACTER VARIETIES OF SURFACE GROUPS AND THE ACTION OF THE TORELLI GROUP
SL(2, C) CHARACTER VARIETIES SURFACE GROUPS TORELLI GROUP
2015/12/17
We determine the action of the Torelli group on the equivariant cohomology of the space of flat SL(2, C) connections on a closed Riemann surface. We show that the trivial part of the action contains t...
COHOMOLOGY OF U(2,1) REPRESENTATION VARIETIES OF SURFACE GROUPS
U(2,1) REPRESENTATION VARIETIES SURFACE GROUPS
2015/12/17
In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2...
Nielsen equivalence of generating sets for closed surface groups
Nielsen equivalence of generating sets closed surface groups
2010/11/29
Generating sets for closed surfaces are either reducible or Nielsen equivalent to a standard generating set.
We study the subgroup structure of the \'etale fundamental group $\Pi$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $\P...
Minimal Lagrangian Surfaces in CH2 and Representations of Surface Groups into SU(2,1)
Minimal Lagrangian Surfaces Representations
2010/12/6
The equation ∂2 ∂z∂¯z log(s2) = |Q|2s−4 + s2 (1.1) is satisfied by the conformally flat metric s2|dz|2 of a minimal Lagrangian surface in the complex hyperbolic plane CH2,...
We show that a surface group contained in a reductive real algebraic group can be deformed to become Zariski dense, unless its Zariski closure acts transitively on a Hermitian symmetric space of tube ...