All Questions
61 questions
3
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158
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What is the meaning of local inertia conjugation property?
In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521, 1-24 (2000). ZBL0953.20030., we have:
Abstract. Let $\widehat{G T}^{1}$ ...
- 119
3
votes
0
answers
282
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Commutator length of the fundamental group of some grope
A popular way to describe a grope as the direct limit $L$ of a nested sequence of compact 2-dimensional polyhedra
$L_0 \to L_1 \to L_2 \to \cdots$
obtained as follows. Take $L_0$ as some $S_g$, an ...
- 2,083
3
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257
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Braids with an infinite number of strings
Has anyone developed a theory for braids with an infinite number of strings?
- 1,181
2
votes
2
answers
151
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How to prove that $\phi: \;\mathrm Mod(S_g)\to \mathrm Sp(2g, \mathbb{Z})$ is an epimorphism? [duplicate]
How do I prove that homomorphism $\phi : \; \mathrm{Mod}(S_g)\to \mathrm{Sp}(2g, \mathbb{Z})$ (induced by the action of mapping class group of a surface on integer homologies of a surface) is an ...
2
votes
1
answer
359
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Induced Map on Sp(2g,Z) is surjective
Let Mg be the Mapping Class Group for $S_g$, the genus-g orientable surface, and consider the action of Mg on $H_1(S_g,\mathbb Z)$ sending f in Mg to m in $Sp^2(2g,\mathbb Z)$ through the induced map ...
- 105
1
vote
1
answer
249
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Name for extension of the symplectic group
Let $S_g$ denote an ortientable surface of genus $g$. Let $\operatorname{Diff}(S_g)$ denote the group of diffeomorphism (that need not fix the orientation). Is there a name for the image of $\...
- 965
1
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1
answer
177
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Intersections of subgroups of surface groups [closed]
Let $\mathcal{S}_g$ denote the fundamental group of an oriented surface of genus $g\ge 2$.
Does $\mathcal{S}_g$ contain subgroups $A$ and $B$ of finite index such that $A\cap B = \lbrace e\rbrace$?
- 35.9k
1
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1
answer
279
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Ways to prove that $n$-component Brunnian link is nontrivial
The attached image shows a way to construct an $n$-component Brunnian link for any $n\geq 3$. That is, this link is not trivial, but deleting any of its components makes the new link trivial. The ...
- 214
1
vote
2
answers
334
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Examples of finite polyhedra with finitely generated simple fundamental group
For $n\geq 2$, $P\mathbb{R}^n$ is a simple example of finite polyhedron with finitely generated simple fundamental group. I was wondering if someone could give me an example of a finite polyhedron ...
- 1,182
1
vote
1
answer
526
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Discrete subgroups of isometry group of proper metric space
Let $X$ be a proper metric space and consider its isometry group $\mathrm{ISO}(X)$ endowed with the compact-open topology. Let $G$ be a subgroup of $\mathrm{ISO}(X)$.
Consider the following ...
- 13
0
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0
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194
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Equivariant cohomology with discrete group action
As far as I know, the equivariant cohomology can be regarded as the generalisation of de Rham cohomology with group action on manifolds. From the literature, the group action is Lie group type. I am ...
