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 6094
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).
5
votes
1
answer
482
views
Knot invariants in 3-manifolds that are not $\mathbb{R}^3$ or $S^3$ or $B^3$?
This is just a reference request; I have no sharp mathematical question.
Inspired by the $(3+)$-year old MO question,
In knot theory: Benefits of working in $S^3$ instead of $\mathbb{R}^3$?,
I would …
- 151k
10
votes
2
answers
2k
views
Do all combinatorially distinct fundamental polygons correspond to surfaces?
The topology of a closed surface can be constructed
by identifying edges of a fundamental polygon of an
even number $2n$ of edges.
Labeling the edges and using $\pm 1$ exponents to indicate
direction, …
- 151k
4
votes
2
answers
837
views
Fundamental polygons with infinite pairwise identifications
The topology of a closed surface can be constructed
by identifying edges of a fundamental polygon of an
even number $2n$ of edges.
Labeling the edges and using $\pm 1$ exponents to indicate
direction, …
- 151k
7
votes
1
answer
415
views
Free $\mathbb{Z}_2$-actions match at some point
I have in front of me a proof of this lemma:
If $f$ and $g$ are free $\mathbb{Z}_2$-actions on $S^1$, then $f(x)=g(x)$ for some $x \in S^1$.
A $\mathbb{Z}_2$-action on the unit circle $S^1$ is a …
- 151k
8
votes
3
answers
1k
views
Is the list of "known" 3D compact manifolds complete?
"it is an open question if the known compact manifolds in 3-D are complete."
This is a quote from Eric Weisstein's
CRC Concise Encyclopedia of Mathematics, Second Edition. 2010, p.480.
(Google Bo …
- 151k
21
votes
1
answer
1k
views
Homeomorphism historically: When did it reach its modern formulation?
Q. When did the notion of homeomorphism reach its
modern formulation as a bicontinuous bijection, i.e., a
continuous bijection
between topological spaces whose inverse is also continuous?
…
- 151k
1
vote
0
answers
156
views
Entangled helical knots
Consider a pair of disjoint, congruent helices $H_1$ and $H_2$
passing through one another in the following sense.
(Caveat lector: This question is not of general interest! It is also long.)
$H_1$ is …
- 151k
3
votes
1
answer
458
views
Surface curves equidistant from a simple closed geodesic
Let $S \subset \mathbb{R}^3$ be a surface embedded in $\mathbb{R}^3$,
let's say (to keep it simple) of genus zero.
Let $\gamma$ be a simple, closed, oriented geodesic on $S$.
Because $\gamma$ is orien …
- 151k
11
votes
4
answers
1k
views
Distance between two knots
Are there some well-studied functions defining natural distance measures between two knots? One can imagine a function that counts, say, the minimum number of
moves, each of which passes one strand of …
- 151k
8
votes
1
answer
717
views
Can any sequence of consecutive integers be realized as winding numbers?
For a closed plane curve $C$, define its sequence of winding numbers to
be the sorted list of the winding numbers of each of the distinct regions
of the plane demarcated by $C$.
For example, this curv …
- 151k
1
vote
0
answers
217
views
Patterns in local winding number sequences
This is something of a followup to an earlier question
Can any sequence of consecutive integers be realized as winding numbers?, whose answer is Yes.
Now I would like to define a local winding number …
- 151k
65
votes
4
answers
4k
views
Tying knots with reflecting lightrays
Let a lightray bounce around inside a cube whose faces
are (internal) mirrors.
If its slopes are rational, it will eventually form a cycle.
For example, starting with a point $p_0$ in the interior
of …
6
votes
0
answers
210
views
"A typical pair of two-dimensional surfaces in four dimensions will intersect at finitely ma...
The title quotes C.H. Taubes in the Princeton Companion to Mathematics (p.404).
I found this surprising despite the natural lower-dimensional analog
(a typical pair of loops in
$\mathbb{R}^2$ will in …
- 151k
1
vote
0
answers
208
views
Fractional degree of a map?
Is there some natural notion of a fractional degree of a map?
The degree of a map is a generalization of the winding number,
and fractional winding numbers appear in the (mathematical physics)
literat …
- 151k
2
votes
1
answer
101
views
Complexity of recognizing equivalent translation surfaces
"A translation surface is a union of polygons with pairs of parallel edges identified by translation, up to cut and paste equivalence."
I take that succinct (and not fully precise) definition fro …
- 151k