Separable subgroups of mapping class groups
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In this paper, a large family of interesting subgroups are shown to be separable from the mapping class group of a surface, such as solvable subgroups, Heegaard and Handlebody groups, geometric subgroups and all the terms in the Johnson filtration.About:
This article is published in Topology and its Applications.The article was published on 2007-01-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: Locally finite group & Sporadic group.read more
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Some problems on mapping class groups and moduli space
TL;DR: In this article, the authors present a number of problems about mapping class groups and moduli space, and present a solution to each of them in the book "Problems on Mapping Class Groups and Related Topics", ed. by B. Farb, Proc. Math. Soc.
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All finite groups are involved in the mapping class group
Gregor Masbaum,Alan W. Reid +1 more
TL;DR: In this article, the orientation-preserving Mapping class group of the genus g 1 closed orientable surface has been studied and it has been shown that every nite group occurs as a quotient of a nite index subgroup of g.
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Proper actions on finite products of quasi-trees
TL;DR: In this paper, it was shown that a finitely generated group $G$ has property (QT) if it acts isometrically on a finite product of quasi-trees so that orbit maps are quasi-isometric embeddings.
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A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
TL;DR: In this paper, it was shown that quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic (and even relatively hyper-bolic in the genus 2 case) under residual finiteness assumptions.
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Dehn filling Dehn twists
TL;DR: In this article, it was shown that composite rotating families can be separable in low complexity in the sense that the action of a group of stabilizers on a hyperbolic graph X is separable from its action on a non-hyperbolic one.
References
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Knots and Links
TL;DR: In this paper, the fundamental group of three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic covers and the Alexander invariant Matrix invariants 3-manifolds and surgery on links Foliations, branched covers, fibrations and so on.
Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
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The Nielsen Realization Problem
TL;DR: In this article, the Nielsen realization problem is answered in the affirmative: every finite subgroup arises as a group of isometries of some hyperbolic surface. But it is not known whether every subgroup of such a group arises as an isotopy class of diffeomorphisms.