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Results tagged with gt.geometric-topology
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user 20516
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
7
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1
answer
198
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Syzygies in Steinberg module of genus 2 mapping class group $\mathrm{MCG}(\Sigma_2)$
$\DeclareMathOperator\MCG{MCG}$Consider the mapping class group $\MCG(\Sigma_2)$ of the closed genus 2 oriented surface $\Sigma_2$. The algebraic-duality theory of $\MCG_2:=\MCG(\Sigma_2)$ is explicit …
- 2,274
6
votes
3
answers
881
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Reference request: embedded Morse theory
For references of embedded Morse theory, or so-called relative morse theory of a pair, I have found R.W. Sharpe's "Total Absolute Curvature and Embedded Morse numbers" totally not helpful. For further …
- 2,274
4
votes
3
answers
570
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Mechanisms generating free subgroups of Artin braid groups
Within my limited experience, I have only known free groups to occur through two mechanisms: as fundamental groups of trees (graphs) and ping-pong. And sometimes only through one way: the fact that su …
- 2,274
3
votes
0
answers
85
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Representing Outer Automorphisms by Outer Matrix Conjugation for MCG?
Let $S$ be closed hyperbolic surface. The Dehn-Neilson theorem $\Gamma \approx Out(\pi_1)$ identifies the mapping class group of $S$ with the outer automorphism group of the surface group $\pi_1=\pi_1 …
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2
votes
1
answer
216
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Is action of MCG on the curve complex computable for closed surfaces? [Yes: Birman Exact Seq...
$\DeclareMathOperator\MCG{MCG}$Let $\Gamma=\MCG(S_{g, 0,0 })$ be mapping class group of closed hyperbolic surfaces. Let $V=C^0(S)$ be the set of vertices of the simplicial curve complex. We are studyi …
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2
votes
Fundamental groups of noncompact surfaces
A new approach to spines is available via mass transport theory and Kantorovich duality. This is developed in my PhD thesis.
The idea is elementary: consider the retract $x\mapsto x/|x|$ from the cl …
- 2,274
2
votes
Syzygies in Steinberg module of genus 2 mapping class group $\mathrm{MCG}(\Sigma_2)$
I recently returned to this question, and have found a formal solution to Closing the Steinberg symbol in genus two using Mark C. Bell's wonderful curver program.
In low genus it was expected that an …
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2
votes
1
answer
332
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density of lagrangian grassmannian in usual grassmannian.
Consider the canonical symplectic structure $(\omega, J)$ on $\mathbb{R}^{2n}$.
(i) What can be said about the density of the lagrangian grassmannian $L$ (i.e. those rank $n$ totally isotropic linear …
- 2,274