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 questions only
not deleted
user 1465
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).
60
votes
6
answers
7k
views
Torsion in homology or fundamental group of subsets of Euclidean 3-space
Here's a problem I've found entertaining.
Is it possible to find a subset of 3-dimensional Euclidean space such that its homology groups (integer coefficients) or one of its fundamental groups is not …
- 4,713
15
votes
1
answer
514
views
Where is the Steenrod Realization problem at?
I'm wondering if there is a more modern reference out there for the Steenrod Realization Problem than the book of Connor and Floyd?
Realizing homology classes in a manifold via embedded submanifolds, …
- 12.9k
5
votes
3
answers
234
views
First usage of the terms pseudo-isotopy and concordance in manifold theory
I am hoping I can use the collective knowledge of the forum to piece together some history. I'm wondering where the terms pseudo-isotopy and concordance originated, in their modern forms as used in ma …
- 19.4k
9
votes
1
answer
374
views
Mapping class groups are finitely generated
Let $N$ be a compact smooth manifold. By "mapping class group" I will mean
$$\pi_0 \operatorname{Diff}(N)$$
i.e. the isotopy-classes of diffeomorphisms of $N$.
My presumption is that this mapping cla …
- 44.4k
3
votes
0
answers
134
views
Isotopy-classes of oriented Schoenflies spheres in $S^4$ is a group under oriented connect-sum
Given two oriented, smoothly-embedded copies of $S^3$ in $S^4$ (called Schoenflies spheres), one can take an oriented connect-sum of the pairs $(S^4, M_1) \# (S^4, M_2)$. This puts a monoidal structu …
- 44.4k
7
votes
2
answers
2k
views
Ideals in the ring of single-variable Laurent polynomials with integer coefficients
I'm writing some software to automatically compute things like Alexander modules, Alexander ideals, Milnor signatures and Farber-Levine pairings for 1 and 2-knot complements. So among other things I …
- 1,446
6
votes
4
answers
1k
views
Generating ribbon diagrams for knots known to be ribbon knots
Is there a source in the literature for ribbon diagrams for the knot-table knots known to be ribbon knots?
For example, I'm interested in doing a computation which needs as input a ribbon diagram for …
- 4,713
13
votes
1
answer
1k
views
Mapping class groups of small Seifert-fibred 3-manifolds
Are computations of the mapping class groups of small Seifert-fibred 3-manifolds recorded in some convenient location?
For most Seifert manifolds working out the mapping class group is easy-enough ( …
- 28.2k
5
votes
0
answers
133
views
Smoothing tame topological knots, from an analytic perspective
A tame topological knot (for the purpose of this question) is a topological embedding of $S^1 \times D^2$ into $\Bbb R^3$.
Tame topological knots are known to be isotopic to smooth knots. This questi …
- 44.4k
12
votes
3
answers
1k
views
Knot theory question: bridge number vs. min generators of fundamental group of complement
Given a knot in the 3-sphere in Bridge Position you can find a presentation for the fundamental group of the complement (a Wirthinger presentation) containing $n$ generators and $n-1$ relators, where …
- 4,713
12
votes
1
answer
639
views
Revisiting Gordon-Luecke theorem
$\DeclareMathOperator\Diff{Diff}\DeclareMathOperator\GL{GL}$Here is an proof-sketch of a strengthened Gordon-Luecke theorem. This is presumably known, but is it written down somewhere? I am also cur …
- 10.5k
25
votes
2
answers
841
views
Which homotopy classes $S^3 \to S^2$ lift to embeddings $S^3 \to S^2 \times D^3$?
The question is, for a smooth embedding
$$f : S^3 \to S^2 \times D^3$$
one can compose the map $f$ with projection $\pi : S^2 \times D^3 \to S^2$, giving the map $\pi \circ f : S^3 \to S^2$.
Which hom …
- 44.4k
32
votes
3
answers
2k
views
A Pachner complex for triangulated manifolds
A theorem of Pachner's states that if two triangulated PL-manifolds are PL-homeomorphic, the two triangulations are related via a finite sequence of moves, nowadays called "Pachner moves".
A Pachne …
- 28.2k
8
votes
0
answers
310
views
Smale's relative h-cobordism theorem
In Smale's On the structure of manifolds paper there is his relative version of the h-cobordism theorem, specifically Theorem 3.1 (and 1.4). Roughly speaking this concerns the situation where one has …
- 44.4k
8
votes
0
answers
173
views
Stratification of space of labelled circles in the plane
Consider the space of $n$ round circles in the plane to be the open subset of $\mathbb R^{3n}$:
$$C_n = \{ (v_1, v_2, \cdots, v_n, r_1, r_2, \cdots, r_n ) : v_i \in \mathbb R^2, r_i \in (0, \infty) \ …
- 151k