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 25510
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).
2
votes
Illumination of a convex body
The answer depends on the point $p$ and on the body. Here is a simple counterexample in $R^3$. Take two regular hexagons in parallel planes, so that the line $L$ connecting their centers is perpendicu …
- 91.8k
4
votes
Accepted
Construction of self-covering map of any surface
First of all, the Riemann-Hurwitz formula with $\chi<0$ implies that
for every self-covering $d=1$ so it is an automorphism. The only punctured surfaces with $\chi\geq 0$ are torus, sphere, and sphere …
- 91.8k
10
votes
Does every orientable surface embed in $\mathbb{R}^{3}$
Here is a reference:
MR0304649 (46 #3781)
Rüedy, Reto A.
Embeddings of open Riemann surfaces.
Comment. Math. Helv. 46 (1971), 214–225.
He talks about Riemann surfaces, but every orientable topological …
- 91.8k
15
votes
Accepted
Do all combinatorially distinct fundamental polygons correspond to surfaces?
Yes. 2. Yes. (I suppose that the surfaces are "the same" if they are homeomorphic).
For 1, it is sufficient to check the definition of surface: that every point has a neigborhood homeomorphic to t …
- 91.8k
4
votes
A convex curve inside the unit circle
This has nothing to do with circles (or polygons). If one convex curve is inside another,
then the length of the inner curve is smaller.
- 91.8k
1
vote
A problem related to connectivity of analytic functions
No, it can be infinite. Start with the function $w=f(z)$ mapping the unit disc onto itself.
Let $I_k$ be disjoint closed arcs on the image disc in the $w$ plane. Deform the image region by adding two …
- 91.8k
3
votes
on common fixed points of commuting polynomials (and rational functions)
I don't know the answers. Consider this as an extended comment.
Let $P$ be the set of fixed points of $g$. Then $f$ maps $P$ into itself.
Indeed let $x\in P$, so $g(x)=x$. Then
$$f(x)=f(g(x))=g(f(x)), …
- 91.8k
32
votes
How would a topologist explain "every Riemann surface of genus $g$ is hyperelliptic if and o...
A 19th century topologist would explain this by dimension count. By Riemann-Hurwitz, a surface of genus $g$ covering the sphere
with $2$ sheets has $2g+2$ ramification points which gives $2g-1$ free c …
- 91.8k
2
votes
Accepted
Existence of covering isomorphism
I suppose that "non-compact complex algebraic curve" means complex affine curve.
The following counterexample was proposed by my friend Fedor Pakovich.
Let $D=\mathbf{C}\backslash\{-1,1\}$.
Consider t …
- 91.8k
2
votes
Maximum of a sum of Gaussian functions
Yes, and this has nothing to do with Gaussian: you can take $\phi_i(x)=g_i(|x-x_i|)$
where $g_i$ are any strictly decreasing functions.
Lemma. If all $x_j$ are all on one side of a hyperplane $H$ (o …
- 91.8k
4
votes
Accepted
Finding a hyperbolic metric with geodesic boundary on a given Riemann surface
A good reference is
W. Abikoff, The real analytic theory of Teichmuller space, Springer, 1980. (Chap. II section 1).
The idea is that you construct the double: it is the result of gluing of your surfa …
- 91.8k
12
votes
Accepted
The behaviour of holomorphic mapping of curves
You are asking too many questions, some of them are very difficult.
Here are some answers.
Image of a Jordan curve under a rational function. Take a circle for $\gamma$.
Every continuous function o …
- 91.8k
3
votes
Jordan curve theorem for cylinders
A more general result is true. Let F and G be two disjoint connected compact subsets
of the sphere. Let D be the component of the complement whose boundary intersects both.
Then D is conformally equiv …
- 91.8k
5
votes
Are there any books/articles that apply abstract coordinate free differential geometry to ba...
There is a calculus textbook which does this:
Bamberg and Sternberg A course in mathematics for students in physics, vol. II,
Chap. 22, "Thermodynamics".
- 91.8k
2
votes
Is it always possible to connect the endpoints of a smooth injective path, so the resulting ...
Solution of your original question: A smooth curve cannot intersect infinitely many times lines in all directions.
Let $\gamma: T\to \Gamma$ be the parametrization
of your curve, where $T$ is the unit …
- 91.8k