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 1358
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).
22
votes
3
answers
3k
views
What is the "serious" name for the topograph (for a quadratic form)
One way to study (mixed signature) quadratic forms in two variables is to study the topograph. Looks like the signature doesn't matter: here is (1,1) and (1-,1).
The name is derived from τοποσ (Gree …
- 22.8k
16
votes
3
answers
5k
views
Mapping Class Groups of Punctured Surfaces (and maybe Billiards)
Where can I find a concrete description of mapping class group of surfaces? I know the mapping class group of the torus is $SL(2, \mathbb{Z})$. Perhaps, there is a simple description for the sphere …
- 22.8k
15
votes
1
answer
2k
views
How to get 3-manifold, Knots from Number Fields
I'm reading a paper On the Torsion Jacquet-Langlands correspondence by Akshay Venkatesh and Frank Calegari.
Truthfully speaking I have no idea what Jacquet-Landlands is. I'm just trying to underst …
- 22.8k
13
votes
2
answers
791
views
"C choose k" where C is topological space
One day I read a generating function in a paper. For any "sufficietly nice topological space", $C$:
$$ \sum_{l \geq 0 } q^{2l}\chi(\mathrm{Sym}^l[C]) = (1 - q^2)^{-\chi(C)} = \sum_{l \geq 0} \binom{ …
- 22.8k
13
votes
1
answer
2k
views
Is there a topograph for Pythagorean triples?
I have been reading Allen Hatcher's notes on quadratic forms. Naturally, we draw a picture encoding all the values of a quadratic form in a topograph. These are build by iterating the parallelogram …
- 22.8k
11
votes
2
answers
1k
views
Thurston-Cannon $S^2$-filling curves
I have been looking into equivariant space-filling curves $S^1\to S^2$ as discussed by Cannon & Thurston in these two papers:
Three-Dimensional Manifolds, Kleinian Groups and Hyperbolic Geometry
Gro …
- 22.8k
9
votes
4
answers
1k
views
Geometry of the space of circles in the Euclidean plane
We know that Mobius transformations, $z\to\frac{az+b}{cz+d}$, permutes circles and lines in the Euclidean plane, $(\mathbb{R}^2, dx^2 + dy^2 )$.
It may even be possible to write an explicit formula …
- 22.8k
9
votes
2
answers
679
views
Examples of automorphic forms over $\mathbb{H}^3/\text{PSL}_2(\mathbb{Z}[i])$
If I understood my automorphic forms correctly, at least cusp forms can be thought of as elements of $L^2(G/\Gamma)$ for a $G = \text{SL}_2(\mathbb{R})$ and $\Gamma = \text{SL}_2(\mathbb{Z})$ or a sui …
- 22.8k
7
votes
5
answers
678
views
Hurwitz Encoding
In "Random Matrices and Random Permutations" by Okounkov it says, "It is classically known that every problem about the combinatorics of a covering has a translation into a problem about permutations …
- 22.8k
6
votes
3
answers
867
views
Find a surface or 3-manifold whose fundamental group is $(\mathbb{Z}/n\mathbb{Z}) \rtimes (\...
I know by Van Kampen's Theorem that we can obtain $\pi_1(S_1 \vee S_1) = \mathbb{Z} * \mathbb{Z}$, so I am wondering if we can construct a surface or 3-manifold whose fundamental group is $\mathbb{Z}_ …
- 22.8k
5
votes
1
answer
352
views
Examples of Morse functions on unit tangent bundle of the sphere $T^1(S^2)$
In a sense, calculus is all about the study of critical points of functions on flat space $\mathbb{R}^N$ (e.g. here). Let's try a different venue, the unit tangent bundle of the sphere.
$$ T^1(S^2) …
- 22.8k
5
votes
0
answers
271
views
deformed Gauss Bonnet formula?
I was reading about Gauss-Bonnet for circles, that integrating the curvature over the circle $\gamma(t)$ leads to the number of times $\gamma'(t)$ rotates around the origin. (The degree of the Gauss …
- 22.8k
4
votes
0
answers
315
views
$ABA^{-1}B^{-1} = E$ the topology of the space of non-commuting matrices
Is there any discussion of topology of space of matrices
$ ABA^{-1}B^{-1} = E $ with $E$ diagonal matrix, $A,B \in \mathrm{GL}(n,\mathbb{C})$?
E.g. is this a variety of just a scheme? How many com …
- 22.8k
4
votes
1
answer
392
views
braids and dynamics of roots of a polynomial
The 2-variable polynomial equation $f(z,t) = 0$ with $z = \mathbb{C}, \\,t \in \mathbb{S^1}$ has $n = \mathrm{deg}_z f$ solutions each fixed $t$. I wanted to follow the roots as they travel with time …
- 22.8k
4
votes
3
answers
222
views
What kind of 3-manifolds arise has hypersurfaces in R^4?
What kind of 3-manifolds can arise as hypersurfaces $\{ f(x,y,z,w) = 0\} \subset \mathbb{R}^4$? Can they have nontrivial H1 or H2?
- 22.8k