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Results tagged with gt.geometric-topology
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user 30679
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).
3
votes
Is there a relative Pachner theorem?
In his paper:
http://arxiv.org/pdf/math/9911256.pdf
Lickorish outlines a proof of theorem (Theorem 5.10) he credits to Pachner and Newman which says that two combinatorial $n$-manifolds with non-empty …
- 574
7
votes
Accepted
"Basic" loops on standardly embedded surfaces
They are often called meridians of $G$. Note that there are many graphs $G$ to which $V$ deformation retracts (most nonplanar); if you are not particular about which graph $G$ then they are called mer …
- 574
3
votes
Surgery along an arc connecting the components of a $2$-component link gives the unknot
A recentish paper of mine (which generalizes portions of Scharlemann's and Eudave-Munoz's work) also addresses this question.
MR3192616 Taylor, Scott A. Comparing 2-handle additions to a genus 2 bo …
- 574
4
votes
Accepted
Classification of tangles?
As Sam Nead points out, there is a relationship between spatial graphs and tangles obtained by drilling out one edge of a spatial graph having two vertices or drilling out the vertex of a spatial grap …
- 574
2
votes
Reference for a theorem on crossing changes of links
The reference is given in the paper you cite:
M. Eudave-Mun ̃oz, Primeness and sums of tangles, Trans. Am. Math. Soc. 306, 773-790 (1988)
The arguments are purely combinatorial, but there should be a …
- 574
7
votes
Is a knotted trivalent graph determined by its set of unzips?
This is really more of a comment, but here goes:
The question you ask is "dual" to this question: Suppose you have two theta graphs $\theta_1$ and $\theta_2$ such that for each edge $e_1$ of $\theta_ …
6
votes
Functoriality of Thurston's norm
For submanifolds that are link complements, Ken Baker and I recently investigated this question in our paper "Dehn Filling and the Thurston Norm" available at arXiv:1608.02443
The basic idea (as in so …
- 574
2
votes
3-manifolds homotopy equivalent to a surface
This paper gives some other very nice counter-examples. As I recall, for open manifolds you really need to think about proper homotopies, not just homotopies.
MR1033220 (91b:57021) Reviewed
Scott, P …
- 574
4
votes
Reference request for wild 3-manifolds
One interpretation of wild/pathological in the 3-manifold setting is noncompact 3-manifolds. Peter Scott and Thomas Tucker have a few lovely papers and in the decades since there have been papers appe …
- 574
4
votes
Accepted
Handlebody decomposition of a 3-manifold adapted to a link
Take a Heegaard splitting of the link exterior and then glue in solid tori with your link components as cores. The Heegaard splitting survives as a Heegaard splitting of the filled manifold and since …
- 574
5
votes
Knot theory in handlebodies of arbitrary genus
If you mean adding 1 and 2 handles to the boundary of the ball, that will never change the (non)triviality of the knot in the 3-ball. On the other hand, perhaps the notion of tunnel number is what you …
- 574