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Results tagged with gt.geometric-topology
Search options questions only
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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).
16
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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
10
votes
2
answers
743
views
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 …
- 23.5k
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. …
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6
votes
1
answer
970
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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
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
9
votes
1
answer
373
views
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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6
votes
0
answers
302
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Cohomology of Zariski neighborhoods
Do there exist smooth compact (=complete) connected complex algebraic varieties $X\subset Y$ and a Zariski neighborhood $U$ of $X$ in $Y$ such that the image of $H^{\ast}(U,\mathbf{Z})$ in $H^{\ast}(X …
- 23.5k
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 …
- 23.5k
9
votes
2
answers
2k
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Embeddings and triangulations of real analytic varieties
This is a follow up question to my answer here How do you define the Euler Characteristic of a scheme?
A real analytic space is a ringed space locally isomorphic to $(X,O/I)$ where $X$ is the zero lo …
- 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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55
votes
3
answers
6k
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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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94
votes
1
answer
11k
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The mathematical theory of Feynman integrals
It is well known that Feynman integrals are one of the tools that physicists have and mathematicians haven't, sadly.
Arguably, they are the most important such tool. Briefly, the question I'd like to …
- 23.5k
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 …
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9
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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 …
- 23.5k
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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