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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...
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...
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...
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...
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...
Index Calculus in Class Groups of Plane Curves of Small Degree
Index Calculus Class Groups Plane Curves Small Degree
2009/2/5
We present a novel index calculus algorithm for the discrete
logarithm problem (DLP) in degree 0 class groups of curves over finite
fields. A heuristic analysis of our algorithm indicates that asymp...
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...