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Results tagged with gt.geometric-topology
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user 2349
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).
8
votes
1
answer
657
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A conjecture of Montesinos
Not every orientable 3-manifold is a double cover of $S^3$ branched over a link. For example, the 3-torus isn't. However, in 1975 Montesinos conjectured (Surjery on links and double branched covers of …
- 23.5k
11
votes
2
answers
1k
views
Number of the Reidemeister moves needed to transform one diagram into another one
A recent question Random Reidemeister moves to unknot contains a link to the paper http://www.ams.org/journals/jams/2001-14-02/S0894-0347-01-00358-7/S0894-0347-01-00358-7.pdf, in which J. Hass and J. …
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8
votes
1
answer
621
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Cohomology map induced by the group actions on homogeneous vector bundles
Here is a topological question which seems quite elementary. The answer to this question may be useful e.g. in estimating the orders of the automorphism groups of some algebraic varieties and in compu …
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18
votes
1
answer
940
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Do chains and cochains know the same thing about the manifold?
This question was inspired by Poincaré quasi-isomorphism
Let $M$ be a closed oriented $n$-manifold. The cap product with the fundamental class of $M$ induces an isomorphism $H^i(M,\mathbf{Z})\to H_{n …
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7
votes
2
answers
390
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Trigonal loci in Teichmueller spaces
Since my previous question
Hyperelliptic loci in Teichmueller spaces
resulted in two quick and helpful replies, let me ask another question in a similar vein:
A smooth compact complex curve is call …
- 23.5k
13
votes
3
answers
954
views
Rational homotopy theory of a punctured manifold
Let $M$ be a smooth simply connected manifold and let $N$ be $M$ minus a point. Is it possible to construct an explicit Sullivan model for $N$ (i.e. a commutative differential graded algebra (cdga) wh …
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6
votes
1
answer
627
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Rational homotopy type of a complement
Let $X$ and $X'$ be smooth closed manifolds. Take closed subpolyhedra $D\subset X$ and $D'\subset X'$ (with respect to some triangulations) and let $f:X\to X'$ be a homotopy equivalence such that $f(D …
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9
votes
5
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1k
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Möbius and projective 3-manifolds
A projective 3-manifold is a smooth manifold that admits an atlas with values in the real projective 3-space such that all transition maps are restrictions of projective transformations. A Möbius 3-ma …
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5
votes
1
answer
448
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Automorphisms of $\pi_1$ induced by pseudo-Anosov maps
Suppose $X$ is an orientable surface with non-empty boundary and $f:X\to X$ is a pseudo-Anosov automorphism that acts identically on $H_1(X,\mathbf{Z})$. Let $x$ be a fixed point of $f$.
For any $\ga …
- 23.5k
61
votes
2
answers
3k
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The topological analog of flatness?
Recall that a map $f:X\to Y$ of schemes is called flat iff for any $x\in X$ the ring $O_{X,x}$ is a flat $O_{Y,f(x)}$-module.
Briefly the question is: what is the topological analog of this?
Many not …
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9
votes
1
answer
373
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Can an action of a compact Lie group be nontrivial if it is trivial on the boundary?
Let $G$ be a compact Lie group acting on a connected topological manifold $M$ with boundary. Suppose the action on one boundary component is trivial. Does it follow that the action on the whole of $M$ …
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5
votes
1
answer
1k
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Which groups admit a unique Lie group structure?
This question is a follow-up on the answer given here Can a Lie group as an abstract group be given more than one topology making it a Lie group?
It is motivated by the following observations:
If $ …
- 23.5k
15
votes
2
answers
967
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Infinity de Rham quasi-isomorphism
This question is similar to Do chains and cochains know the same thing about the manifold? in the sence that both deal with a natural "comparison" quasi-isomorphism that does not preserve the ring str …
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14
votes
4
answers
1k
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Mappings of mapping class groups
Let $X$ be a compact non-orientable surface, maybe with boundary, and let $\tilde X$ be the orienting cover of $X$. If I understand correctly, any smooth automorphism of $X$ lifts naturally to an auto …
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21
votes
3
answers
2k
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Cohomology of fibrations over the circle: how to compute the ring structure?
This question is inspired by Cohomology of fibrations over the circle Moreover, it can be considered a subquestion of the above, but somehow it seems to me that some of the more interesting points wer …
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