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Results tagged with gt.geometric-topology
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user 2669
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).
12
votes
3
answers
1k
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Is there a procedure for obtaining all knots in S^3?
(Just to be precise, in this question, the word "knot" means "ambient isotopy class of a (EDIT: smooth) knot in $S^3$.") A knot in $S^3$ is called prime if it is not the connected sum of two other non …
- 2,869
28
votes
3
answers
4k
views
Complete knot invariant?
I've seen a couple papers (that I now can't find) that say that in his paper "On irreducible 3-manifolds which are sufficiently large" Waldhausen proved that the data $\pi_1(\partial (S^3\setminus K)) …
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3
votes
Gap in Przytycki's computation of the skein module of links in a handlebody?
Here's something that isn't a complete rigorous proof, but maybe it can be completed to one (unless I'm missing something). Let's fix a non-positively curved metric on $F$ (which rules out the sphere, …
- 2,869
2
votes
2
answers
650
views
Do homeomorphisms of boundary components of 3-manifolds extend to the manifold?
The question that I'd like to answer can be generalized to the following: if $M$ is an orientable 3-manifold and $F$ is a boundary component of $M$ (which may have other boundary components), can an a …
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2
votes
0
answers
129
views
Is there an analog of Reidemeister's theorem for braids in a surface?
Reidemeister's classical theorem describes the set of links in $\mathbb R^3$ up to isotopy as the set $\{ \textrm{diagrams in } \mathbb R^2\textrm{ with crossings}\}$ modulo certain local relations on …
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8
votes
The Jones polynomial at specific values of $t$
The volume conjecture predicts the existence limit of (a certain normalization of) the colored Jones polynomials evaluated at roots of unity (which is not known to exist), and that this limit is equal …
- 2,869
16
votes
Accepted
Jones polynomial of the concatenation of two braids
Here is one reason not to expect such a relationship (although I'm not sure if it can be completed to a proof). The Jones polynomial $J_\sigma$ (roughly) comes from taking the trace of a linear map $A …
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12
votes
Proving that the Jones polynomial is q-holonomic
One statement that would imply that the colored Jones polynomials are q-holonomic involves the Kauffman bracket skein module $S_q(K)$ of the knot complement. This is a module over the skein module of …
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