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Results tagged with gt.geometric-topology
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user 1441
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).
13
votes
1
answer
861
views
Ramified cover of 4-sphere
Is it true that any closed oriented $4$-dimensional manifold can be obtained as a result of the following construction:
Take $S^4$ with a finite collection of immersed closed 2-manifolds (with trans …
- 45k
18
votes
2
answers
1k
views
Which immersed plane curves bound an immersed disk?
I am looking for a nice answer to the following question.
Which immersed plane curves bound an immersed disk?
Comments.
I am not sure what is a nice answer, but for sure I could make a stupid …
- 45k
20
votes
2
answers
1k
views
Rugged manifold
It is well known that any compact smooth $m$-manifold can be obtained from $m$-ball by gluing some points on the boundary.
Is it still true for topological manifold?
Comments:
To proof the smo …
- 45k
10
votes
1
answer
387
views
Wild half-line in a Euclidean space
Is there an $m$-dimensional simplicial complex $S$ with the following properties:
The cone over $S$ is homeomorphic to $\mathbb{E}^{m+1}$. Here $\mathbb{E}^{m+1}$ denoes the $(m+1)$-dimensional Eucl …
- 45k
24
votes
4
answers
4k
views
Fundamental group of 3-manifold with boundary
Is it true that any finitely presented group can be realized as fundamental group of compact 3-manifold with boundary?
- 45k
3
votes
1
answer
322
views
Simplified Bing's house
Bing's house is an example of contractible 2-complex in $\mathbb{R}^3$.
One may think that it is a surface without boundary that has two types of singularities: tripod curves — curves where three piec …
- 45k
9
votes
1
answer
340
views
Ramified cover of 3-ball
I it true that any connected oriented 3-manifold with nonempty boundary can be obtained as a ramified cover of 3-ball with a ramification at a link?
link = a 1-dimensional submanifold with possibly …
- 45k
15
votes
1
answer
410
views
bi-Lipschitz gluing
Let $H$ be the Heisenberg group with
left invariant sub-Riemannian metric and $\varepsilon>0$ is small.
Let us denote by $|x-y|_H$ the distance from $x$ to $y$ in $H$.
I have a bi-Lipschitz homeomor …
- 45k
13
votes
1
answer
562
views
Limit of homeomorphisms from square to square
Let $\square=[0,1]\times[0,1]$ be the unit square
and $f\colon\square\to \square$ is a continuous map that fixes the points on the boundary.
Assume $f$ is a limit of homeomorphisms $\square\to \squar …
- 45k
17
votes
1
answer
573
views
Simply connected slices
Assume $\Omega$ is an open set in $\mathbb R^3$
such that the intersection of $\Omega$ with any horizontal plane is simply connected.
Can you prove that $\Omega$ is simply connected?
(Note th …
- 45k
16
votes
2
answers
813
views
Klee's trick --- more applications
In his "Some topological properties..." (1955), Klee gave a construction (simple and beautiful) of an isotopy $h_t\colon\mathbb{R}^{2\cdot n}\to \mathbb{R}^{2\cdot n}$ which moves any compact set $K$ …
- 45k
6
votes
1
answer
301
views
Stable torus that is not a torus [duplicate]
Let $M$ be a closed manifold such that $M\times \mathbb{S}^1$ is a torus.
Is it true that $M$ is homeomorphic to a torus?
- 45k