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Results tagged with gt.geometric-topology
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user 6205
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).
37
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0
answers
2k
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What is the three-dimensional hyperbolic volume of a four-manifold?
Every smooth closed orientable 4-manifold may be constructed via a handle decomposition. Before asking a couple of questions, I recall some well-known facts about handle-decompositions of 4-manifolds. …
- 10.5k
28
votes
4
answers
2k
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Can all n-manifolds be obtained by gluing finitely many blocks?
Fix a dimension $n\geqslant 2$. Let $S= \{M_1,\ldots, M_k\}$ be a finite set of smooth compact $n$-manifold with boundary. Let us say that a smooth closed $n$-manifold is generated by $S$ if it may …
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24
votes
2
answers
2k
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Explicit homeomorphism between Thurston's compactification of Teichmuller space and the clos...
Thurston's celebrated compactification of Teichmuller space was first described in his famous Bulletin paper. Teichmuller space is famously homeomorphic to an open disc of some dimension (this can be …
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21
votes
6
answers
3k
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Is there a good notion of morphism between orbifolds?
Following Thurston, an orbifold is a topological space which looks locally like a finite quotient of $\mathbb R^n$ by a finite group of $O(n)$: this is expressed using charts as for differentiable m …
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19
votes
0
answers
847
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Which manifolds decompose into pants?
In this nice paper Mikhalkin uses certain (more geometrical than algebraic) aspects of tropical geometry to prove that every complex projective hypersurface in $\mathbb C \mathbb P ^n$ decomposes as a …
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17
votes
1
answer
2k
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Proofs of Rohlin's theorem (an oriented 4-manifold with zero signature bounds a 5-manifold)
A celebrated theorem of Rohlin states the following
An oriented closed 4-manifold $M^4$ bounds an oriented 5-manifold if and only if the signature of $M^4$ is zero.
Simple homological arguments …
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16
votes
2
answers
606
views
Does a small-area sphere in a 3-manifold bound a small ball?
Let $M$ be a closed riemannian 3-manifold. I think that the following fact should be true and should have a relatively simple proof, but I cannot figure it out.
For every $\varepsilon>0$ there is …
- 10.5k
15
votes
3
answers
832
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Maximal euler characteristic of surfaces bounding two fixed curves
Let $\gamma_0$ and $\gamma_1$ be two simple closed curves in a closed surface $S$.
What is the maximum Euler characteristic of a compact properly embedded surface $\Sigma \subset S\times [0,1]$ s …
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12
votes
3
answers
1k
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Is the cut locus of a generic point in a hyperbolic manifold a generic polyhedron?
Let $p\in M$ be a point in a closed riemannian manifold $M$. Recall that the cut locus of $p$ is the subset of $M$ consisting of all points that are connected to $p$ by at least 2 distance-minimizing …
- 10.5k
11
votes
0
answers
354
views
Fox re-imbedding theorem in dimension four
Fox re-imbedding theorem states the following:
A compact 3-manifold $M$ with boundary that embeds in the three-sphere $S^3$, can be re-imbedded in $S^3$ so that its complement is a union of handle …
- 10.5k
10
votes
1
answer
566
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Is the spectrum of closed geodesics in a closed hyperbolic 3-manifold asymptotically homogen...
It seems to me that the results in this important paper of Kahn-Markovich imply the following fact. Let $M^3$ be any closed hyperbolic 3-manifold. For every $\epsilon > 0$ there is a natural number $R …
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9
votes
0
answers
135
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Is there a closed aspherical manifold with infinitely many symmetries and without essential ...
The precise question is the following:
Is there a closed aspherical manifold $M$ of dimension $n\geq 3$ such that Out($\pi_1(M)$) is infinite and $\pi_1(M)$ does not contain $\mathbb Z \times \mathbb …
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