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These notes are based on lectures given at Zhejiang University, July 14–20, 2008. My goal was to present some analytic techniques that can be used to study the action of the mapping class group on the...
Let be a compact orientable surface with genus g andnboundary components ∂1,..., ∂n. Let b = (b1,...,bn) ∈ [−2,2] n. Then the mapping class group Mod() acts on the relative SU(2)-...
When G is a connected compact Lie group, and π is a closed surface group, then Hom(π, G)/G contains an open dense Out(π)-invariant subset which is a smooth symplectic manifold.
Deformation spaces Hom(π, G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group ModΣ, preserving a Poisson structure. Wh...
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spinc-structure is faithful. The paper is self-contained, and in particular does not assume any ...
The Torelli group, I(Sg), is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface.
Given a Lagrangian sphere in a symplectic 4-manifold (M, ω) with b+ = 1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension of (M, ω) is −∞, this result t...
We compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We...
We compute the stable cohomology of the universal Picard stack Pic g ! M g, and also its Picard group. The degree zero Picard stack Pic0 g has homotopy type the classifying space of Kawazumis extende...

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