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Results tagged with gt.geometric-topology
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user 89741
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).
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129
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When is a nested sequence of closed sets a colimit?
Let $X$ denote a topological space and $X_0\subset X_1\subset \ldots\subset X$ a nested sequence of closed subsets of $X$ such that $$ \bigcup_i X_i =X$$
It is easy to see that in the general case $X …
- 1,174
0
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1
answer
166
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Mappings of reducible 3 manifolds with boundary
In section 3 of his paper "Mappings of reducible 3 manifolds" McCullough, proves that every self-homeomorphism of a reducible 3 manifold can up to isotopy be written as a composition of particularly n …
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0
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Bounded cohomology motivation
Even though this is an old question, I want to add a different answer by saying that to me personally bounded cohomology in itself is not very interesting. It tends to be infinite dimensional or zero. …
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11
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2
answers
668
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Can we embed a closed manifold into a homotopy equivalent CW complex?
Suppose $X$ is a CW complex and $M$ is a closed manifold and suppose further that there exists a homotopy equivalence $X \simeq M$. Does there exists an embedding of $M$ into $X$ (i.e. an injective (p …
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2
votes
1
answer
118
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Hyperbolization with word-hyperbolic fundamental group
In Davis-Januszkiewica´s paper Hyperbolization of polyhedra it is shown that for every manifold $M$ there exists a map $N \to M$ of non-zero degree such that $N$ is aspherical (plus some more properti …
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6
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Can we embed a closed manifold into a homotopy equivalent CW complex?
While thinking about it with a friend, we came up with the following two dimensional counter example:
Take the standard knot diagram of the trefoil knot (as a self-intersecting curve in $\mathbb{R}^2$ …
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8
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0
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219
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Representing the fundamental class of an aspherical manifold in the bar complex
Suppose $M$ is a compact orientable aspherical manifold and $G$ its fundamental group. Is there a nice description of representatives of the fundamental class of $M$ and its dual in the (homogenous) b …
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5
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1
answer
231
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Amenable link groups
The unknot and the Hopf link are (as far as I know) the only links whose complements have abelian fundamental groups. Are there more examples whose complement have amenable fundamental group?
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5
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1
answer
316
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0-surgery on a fibered hyperbolic ribbon knot
Does there exist a fibering hyperbolic ribbon knot such that the 0 surgery is exceptional? If so does there exist such an example where the result of 0-surgery is Seifert fibered?
I tried looking at k …
- 1,174
7
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0
answers
317
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Different definitions of Stiefel-Whitney classes
It is quite easy to show that different definitions of the Stiefel-Whitney classes agree by showing that they satisfy the well-known axioms. Nevertheless I have been asking myself wether one can prove …
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9
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1
answer
434
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Action of diffeomorphism group on non-vanishing vector fields
Let $M$ denote a closed manifold. Let $\Gamma(TM\setminus 0) $ denote the space of non-vanishing sections of $TM$. Note that the diffeomorphism group $\text{Diff} (M)$ acts on $\Gamma(TM\setminus 0 …
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10
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3
answers
656
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Doubles of 2-handlebodies
Let $X$ denote a $4$-manifold with boundary obtained by adding $k_1$ $1$-handles to $B^4$ and $k_2$ many $2$-handles to the resulting manifold i.e. $X$ is an arbitrary $4$-dimensional $2$-handlebody. …
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Accepted
Doubles of 2-handlebodies
Let $X$ denote a $2$-handlebody. I claim that the inclusion $\partial X \to X$ induces a surjection on fundamental groups. Indeed, let $Y\subset X$ denote the underlying $1$-handlebody (i.e. the union …
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12
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1
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368
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Fundamental group of the complement of a codimension two submanifold
Let $M$ denote an arbitrary closed, connected, n-dimensional manifold for $n\geq 4$. Does there always exist a closed (not necessarily connected!) codimension two submanifold $S \subset M$ such that $ …
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