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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
THE ACTION OF THE MAPPING CLASS GROUP ON REPRESENTATION VARIETIES
MAPPING CLASS GROUP REPRESENTATION VARIETIES
2015/12/17
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...
ERGODICITY OF MAPPING CLASS GROUP ACTIONS ON SU(2)-CHARACTER VAR IET IES
GROUP ACTIONS MAPPING CLASS
2015/9/29
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)-...
THE MAPPING CLASS GROUP ACTS REDUCIBLY ON SU(n)-CHARACTER VARIETIES
CLASS GROUP ACTS REDUCIBLY VARIETIES
2015/9/29
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.
MAPPING CLASS GROUP DYNAMICS ON SURFACE GROUP REPRESENTATIONS
GROUP DYNAMICS GROUP REPRESENTATIONS
2015/9/29
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...
On visualization of the linearity problem for mapping class groups of surfaces
visualization linearity problem mapping class groups surfaces
2012/3/1
We derive two types of linearity conditions for mapping class groups of orientable surfaces; one for once-punctured surface, and the other for closed surface, respectively. For the once-punctured case...
A faithful linear-categorical action of the mapping class group of a surface with boundary
faithful linear-categorical action mapping class group surface with boundary
2011/1/18
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.
New series in the Johnson cokernels of the mapping class groups of surfaces
New series Johnson cokernels mapping class groups of surfaces
2011/1/20
Let g,1 be a compact oriented surface of genus g with one boundary component,andMg,1 its mapping class group. Morita showed that the image of the k-th Johnson homomorphism M
k of Mg,1 is contained ...
Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
Lagrangian spheres symplectic surfaces symplectic mapping class group
2011/2/22
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...
Number of pseudo--Anosov elements in the mapping class group of a four--holed sphere
Mapping class group growth series growth functions
2010/12/21
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...
Stable cohomology of the universal Picard varieties and the extended mapping class group
moduli spaces Picard variety stable cohomology
2011/1/18
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 Kawazumi’s extende...
Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. O...
A sharp bound on fixed points of surface symplectomorphisms in each mapping class
sharp bound fixed points of surface symplectomorphisms
2010/11/29
Given a closed, oriented surface , possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of xed points of a surface symplectomorphism (i.e. area-preserving map) in ...
Low-dimensional homology groups of mapping class groups: a survey
Low-dimensional homology groups mapping class
2010/3/1
In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co) homology are also mentione...