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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).
14
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4
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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 …
- 63.9k
16
votes
0
answers
324
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Rational equivalence of smooth closed manifolds
All spaces below will be assumed simply connected. A continuous map is a rational equivalence if it induces an isomorphism of the rational homology groups. Two spaces are rationally equivalent if they …
- 23.5k
55
votes
3
answers
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Kirby calculus and local moves
Every orientable 3-manifold can be obtained from the 3-sphere by doing surgery along a framed link. Kirby's theorem says that the surgery along two framed links gives homeomorphic manifolds if and onl …
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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 …
- 35.5k
25
votes
2
answers
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Proofs of Kirby's theorem
Each orientable 3-manifold can be obtained by doing surgery along a framed link in the 3-sphere. Kirby's theorem says that two framed links give homeomorphic manifolds if and only if they are obtained …
- 35.5k
11
votes
2
answers
1k
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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. …
CommunityBot
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votes
7
answers
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CW-structures and Morse functions: a reference request
The following is probably well known, but I wasn't able to locate a reference in the literature.
Let $f$ be a Morse function on a smooth compact manifold $M$ without boundary and let $\rho$ be a Rie …
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9
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5
answers
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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 …
- 26.3k
19
votes
2
answers
887
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Lie algebra automorphisms and detecting knot orientation by Vassiliev invariants
Recall that there are knots in $\mathbf{R}^3$ that are not invertible, i.e. not isotopic to themselves with the orientation reversed. However, it is not easy to tell whether or not a given knot is inv …
CommunityBot
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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 …
- 53.3k
10
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2
answers
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Embedded (framed) cobordisms
[The title initially was "Actions of gauge groups on framed cobordisms. This has been changed.]
This question is a follow-up to my answer to When is a submanifold of $\mathbf R^n$ given by global equ …
CommunityBot
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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 …
CommunityBot
- 1
29
votes
5
answers
7k
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Proof of the Reidemeister theorem
While preparing for my introduction to topology course, I've realized that I don't know where to find a detailed proof of the Reidemeister theorem (two link diagrams give isotopic links, iff they can …
- 2,235
13
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3
answers
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Hyperelliptic loci in Teichmueller spaces
Let ${\cal M}_g$ be the moduli space of smooth complex genus $g$ curves, let ${\cal H}_g\subset {\cal M}_g$ be the hyperelliptic locus and set ${{\cal H}}'_g$ to be the preimage of ${\cal H}_g$ in the …
- 68.9k
6
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1
answer
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Constructible sheaves and dg-modules
Let $M$ be a smooth manifold, $A_M$ the de Rham algebra of $M$, $D_{A_M}$ the derived category of the category of differential graded (dg) $A_M$-modules and $D^+_c(M)$ the bounded below constructible …
- 23.5k