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Results tagged with gt.geometric-topology
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user 124004
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).
6
votes
Accepted
Is the dimension given by Klee trick ever sharp?
Are the embeddings required to be isometric embeddings? If not, then what about including three points into $\mathbb{R}$ in two ways, so that the middle point of the three changes? More explicitly, …
- 3,451
5
votes
Can a cyclic group of prime order act on a rationally acyclic finite dimensional complex and...
I needed a slightly more complicated example than this in a paper of mine, so I included a proof there. For any non-trivial finite group $Q$ I give a 3-dimensional rationally acyclic complex with a …
- 3,451
3
votes
What is the minimal dimension of a complex realising a group representation?
This does not answer Greg's question, but it is related. You can realize any $\mathbb{Z}G$-module you that like as $H_1$ of a based 2-complex, or as $H_2$ of a 3-complex if you insist that the comple …
- 3,451
3
votes
Groups acting on products of hyperbolic spaces
This question for a product of one Gromov hyperbolic space is a famous open problem (see for example Bestvina's problem list) and as far as I am aware the general case is also open.
- 3,451
12
votes
Accepted
Quotient of solid torus by swapping coordinates on boundary
Your quotient manifold is homeomorphic to $S^3$. I know this because it is a closed 3-manifold and its fundamental group is trivial, so I'm quoting the Poincare conjecture/Perelmann's theorem. The f …
- 3,451
8
votes
Accepted
Status of the Hopf-Thurston sign conjecture in dimension 4
There has been a lot of work on cases of this conjecture connected to Coxeter groups. M. Davis and R. Charney made a conjecture that comes from these cases in 1995 in The Euler characteristic of a no …
- 3,451
6
votes
Is there a contractible hyperbolic 3-orbifold of finite volume?
As pointed out by Moishe Kohan in the comments below, the following doesn't answer the question as asked, because my group $\Gamma$ is not contained in $SO(3,1)$. Anyway, here is an easy description …
- 3,451