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Results tagged with gt.geometric-topology
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user 21985
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).
1
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0
answers
82
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Proper actions on unitary spheres of a Hilbert space
Free group action of spheres, or products of spheres by finite groups have been studied extensively in the literature, giving in many cases restrictions to the cohomological pro …
- 2,630
1
vote
1
answer
127
views
Homotopy of Unitary sphere in a Banach space and finite dimensional spheres
Let $E$ be a Banach space, $X_1, X_2, \ldots $ be a numerable collection of
finite dimensional subspaces $X_1\subset X_2$ with dimension
tending to infinity, denote by $S^n$ the u …
- 2,630
2
votes
1
answer
162
views
Structure sets for three dimensional surgery
Is there a treatment in the literature of the structure sets relating simple homotopy equivalences to homeomorphisms in the three dimensional case? I am aware that due to the geo …
- 2,630
2
votes
0
answers
90
views
Simple homotopy type of interval bundles over surfaces
Consider a locally trivial (topological) bundle over the Klein bottle
$$ I\to E \to K$$
The projection map $E \to K$ is a homotopy equivalence.
Is it a simple homotopy equivalence?
Du …
- 2,630
4
votes
1
answer
330
views
Ends of Coxeter Groups
It is known after Stallings that a group can have 0, 1, 2 or infinitely many ends. Are there known results on the space of ends of a Coxeter group?
- 2,630
1
vote
0
answers
72
views
Asymptotic dimension of Bicombable groups
Do Bicombable Groups have finite asymptotic dimension?
- 2,630
10
votes
0
answers
367
views
Steenrod Problem and realization of rational homology classes by manifolds
Steenrod's problem asks wheter a simplicial homology class of a topological space $x$,
$$ x\in H_n(X, \mathbb{Z})$$
can be represented by a triangulation of an $n$-dimensional, close …
- 2,630
5
votes
1
answer
207
views
homological 2 dimensional groups
In a Commentarii Mathematici Helvetici paper by Benno Eckman and Heinz Müller in 1980 (volume 50, pages 510-520) proved that poincaré Duality Groups of dimension 2 with positive first Bet …
- 2,630
5
votes
0
answers
148
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Higher homotopy groups and ramified covering maps [duplicate]
It is known in elementary algebraic topology that a covering map induces an isomorphism of higher homotopy groups.
Is there any relation of the higher homotopy groups of the …
- 2,630
6
votes
1
answer
142
views
Example of nonvanishing Waldhausen Nil group
In a remarkable series of papers, both anticipating development in geometric topology and algebraic K-theory, specifically what we call now the Farrell-Jones conjecture, Waldhausen intr …
- 2,630
3
votes
1
answer
74
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Conjugacy of topological actions on aspherical three manifolds to isometric actions
Edited: Due to work of Raymond and Scott, there exist diffemorphisms (of certain three-dimensional nil-manifolds) whose $n$th power is diffeotopic to the identity, but which are not themselves …
- 2,630
4
votes
1
answer
118
views
Enumeration of three dimensional spherical good orbifolds covered by Nil, sol and E3
Is there in the literature a list of three dimensional spherical, good orbifolds covered by nil, Sol and E3, and their algebraic topological invariants? (Homology, orbifold fundamental group).
- 2,630
2
votes
0
answers
67
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Cohomological dimension of closed $G$-invariant subspaces on homology manifolds with a group...
Suppose $G$ is a compact topological group acting on an $m$-homology manifold $M$ over some ring $R$ by homeomorphisms.
Assume that the action of $G$ is effectively finite on a closed $ …
- 2,630
10
votes
1
answer
1k
views
Acyclic Finite Groups
A group is called acyclic if its classifying space has the same homology of a point. Examples of acyclic groups include Higman's group with four generators and relations, also kno …
- 2,630
10
votes
1
answer
973
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Status of Zeeman's collapsability Conjecture
Zeeman's conjecture in topological combinatorics states that if $K$ is a contractible polyhedron of dimension 2, then $K\times I$ has a collapsible subdivision.
What is the status of this …
- 2,630