Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with gt.geometric-topology
Search options answers only
not deleted
user 6205
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).
42
votes
Accepted
Kirby calculus and local moves
There is a finite set of local moves. For instance, these:
(source: unipi.it)
In the second row, the number of encircled vertical strands is $n\leqslant 3$ on the left and $n\leqslant 2$ on the right …
- 10.5k
21
votes
Applications of knot theory
If you manage to convince your students that smooth manifolds are among the most beautiful and interesting objects in mathematics, expecially dimensions 3 and 4 that model our universe, then you can s …
20
votes
fundamental group and complete invariant of irreducible 3-manifolds
Perelman has proved Thurston's geometrization conjecture, which says that every irreducible 3-manifold decomposes along its canonical decomposition along tori into pieces, each admitting a geometric s …
- 10.5k
19
votes
Does there exist a closed manifold that can be given both a Euclidean and a Hyperbolic struc...
This is impossible. By Bieberbach's Theorem a flat closed $n$-manifold $M$ has a finite cover which is a flat $n$-torus. This implies that $M$ contains a (finite-index) subgroup isomorphic to $\mathbb …
- 10.5k
18
votes
Can knot diagrams be monotonically simplified using under moves?
This is just a comment. The same week (!) when Dylan asked this question, we received at our department a message from a non-professional mathematician who wrote a computer program that tries to simpl …
- 10.5k
15
votes
Accepted
Can we embed a closed manifold into a homotopy equivalent CW complex?
Pick a torus, and add two discs along a meridian and a longitude. You get a 2-complex homotopic to a sphere that does not contain a sphere. This generalises easily to any genus by picking a genus-$g$ …
- 10.5k
15
votes
Accepted
Topological characterisation for a (closed irreducible) hyperbolic 3-manifold
A clear statement is the following:
A compact 3-manifold $M$ is hyperbolic if and only if it has infinite fundamental group and does not contain any essential surface with $\chi \geqslant 0$.
Yo …
- 10.5k
14
votes
In knot theory: Benefits of working in $S^3$ instead of $\mathbb{R}^3$?
One may freely pass from $S^3$ to $\mathbb R^3$ just by adding/removing a point; however $S^3$ is nicer when using 3-dimensional topology techniques, in particular geometrization.
For instance, the co …
- 10.5k
14
votes
Examples of acylindrical 3-manifolds
You are looking for
compact 3-manifolds that admit a hyperbolic metric with geodesic boundary
equivalently
compact 3-manifolds that do not contain any essential surface with $\chi \geq 0$
…
- 10.5k
13
votes
Is the topological concept of collapsible useful?
There is a simple reason for appreciating collapsible objects: a collapsible (PL) n-manifold is always (PL) homeomorphic to a disc! (Although a contractible one may not, for instance in dimension 4.) …
- 10.5k
13
votes
Is every real n-manifold isomorphic to a quotient of $\mathbb{R}^n$?
Every closed (that is, compact without boundary) smooth connected manifold $M$ is a quotient of some $\mathbb R^n$. Put on $M$ an arbitrary riemannian metric. A metric on a compact manifold is necessa …
- 10.5k
13
votes
Is there a way to classify incompressible surfaces in $\Sigma \times [0,1]$ ?
It is a difficult problem and as far as I know there is no general answer. Topologists usually look for incompressible and $\partial$-incompressible surfaces, and in that case there are only horizon …
- 10.5k
12
votes
Accepted
Impossibility of realizing codimension 1 homology classes by embedded non-orientable hypersu...
If $[\Sigma]\in H_{n}(M,\mathbb Z)$ is primitive, its image $[\Sigma] \in H_{n}(M,\mathbb Z/2\mathbb Z)$ can always be represented by a non-orientable manifold! Since it is primitive, we may suppose …
- 10.5k
11
votes
Accepted
What constant ensures hyperbolicity of Dehn surgery?
Given a hyperbolic link $L$, Thurston's Dehn filling theorem says that there is a finite set of "bad slopes" on each component of $L$ such that every filling avoiding them is hyperbolic. A slope is ju …
- 10.5k
11
votes
Hyperbolic Brunnian links and rectangular cusp shapes
The rectangular shapes that you find are probably due to the particular symmetries these links have. When there is a symmetry that fixes a component $C$ of a link which fixes both the meridian and the …
- 10.5k