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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...
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 ...
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...
For every positive integer n, we exhibit a cofinite subgroup Gn of the mapping class group of a surface of genus at most two such that Gn admits an epimorphism onto a free group of rank n. We conclude...
Conjugacy Classes of Finite Subgroups of Certain Mapping Class Groups
Hyperelliptic mapping class group finite subgroups of mapping class group
2010/2/26
We give a complete description of conjugacy classes of finite subgroups of the mapping class group of the sphere with r marked points. As a corollary we obtain a description of conjugacy classes of ma...
On the Linearity of Certain Mapping Class Groups
Mapping class groups Braid groups Linear groups
2010/3/1
S. Bigelow proved that the braid groups are linear. That is, there is a faithful representation of the braid group into the general linear group of some field. Using this, we deduce from previously kn...