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Results tagged with gt.geometric-topology
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user 6514
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).
16
votes
Constructing 4-manifolds with fundamental group with a given presentation.
Taking the boundary of tubular neighborhood in codimension two doesn't preserve fundamental group -- the codimension must be at least three.
For a simple example, if you take the boundary of a tubula …
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7
votes
Accepted
Extending a map from $S^n\to M^n$ to a nice map from $B^{n+1}\to M^n$
The answer is no, essentially since higher homotopy groups of spheres are nontrivial.
For example, in the $n=3$ case let $M=B^3$ and let $\sigma\colon S^3 \to M$ be the Hopf map from $S^3$ to the bou …
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9
votes
Accepted
Growth rates of surface groups
Just to make the method as concrete as possible, I'll compute the growth rate for the fundamental group $G$ of a surface of genus two. The Cayley graph of $G$ is the 1-skeleton of a tiling of the hyp …
- 8,483
18
votes
Folner sets and balls
This is not exactly an answer to the question, but is instead essentially a comment that was way too long for the comment space.
The OP mentioned that he doesn't have a good sense for the shapes of F …
- 8,483
4
votes
Accepted
Starting letters of equivalent infinite geodesic paths of hyperbolic Coxeter groups
This is false. The archetypical family of hyperbolic Coxeter groups are the hyperbolic triangle groups
$$
T(l,m,n) = \langle a,b,c \mid a^2=b^2=c^2=(ab)^l=(bc)^m=(ca)^n=1\rangle
$$
where $l,m,n\geq 2 …
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8
votes
Accepted
Asymmetry of outer space - injectivity radius
Given a geodesic metric space $X$ and a point $p\in X$, the injectivity radius $\mathrm{injrad}(p)$ is the maximum value of $r$ such that every point in the open ball $B(p,r)$ is connected to $p$ by a …
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7
votes
2
answers
342
views
Convex subcomplexes of CAT(0) cubical complexes
Is the following statement true? If so, can anyone provide a reference?
Let $X$ be a CAT(0) cubical complex, and let $Y$ be a connected
subcomplex of $X$. Then the following are equivalent:
…
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