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).
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
9
votes
Computation on characteristic classes
There is a great theorem proved by Halperlin - Toledo, which says that if you have a triangulated manifold $M$, you can represent combinatorially every Stiefel - Whitney class $w^k(M) \in H^k(M, \math …
- 10.5k
2
votes
A neighborhood of a 2-disc $D\subset\Bbb R^4$ that tapers off towards the boundary?
Pick a triangulation of $\mathbb R^4$ which contains $D$ as a subcomplex, make two barycentric subdivisions, and then pick the closure of all the simplexes that intersect the interior of $D$. This cou …
- 10.5k
2
votes
Accepted
An equivalence relation on knots similar to concordance
Take a knot, and another copy of the same knot far away. It is then a nice instructive exercise to prove that if they are not unknots they do not cobound annuli.
- 10.5k
6
votes
Injectivity of map of fundamental groups from totally geodesic hypersurface
You need $X_0$ to be closed inside $X$, otherwise, the theorem is false (there are simple counterexamples). So let us suppose that $X_0$ is closed.
Inclusions give the induced homomorphisms
$$\pi_1(X_ …
- 10.5k
6
votes
Accepted
Revisiting Gordon-Luecke theorem
I think that the correct theorem should be the following:
If $L$ does not contain any split unknot or any two coaxial components, the image of the map is finite
Following Cameron Gordon, two coaxial …
- 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
9
votes
Accepted
Dehn surgery along primitive knot in 3-dimensional handlebody
Since $c\subset H_g$ intersects an essential disc $D$ in a single point, the boundary of a regular neighbourhood of $D\cup c$ is another disc $D'$, which splits $H_g$ into a solid torus containing $D\ …
- 10.5k
6
votes
Cell structures of Dold manifold and Wu manifold
The 1965 paper Simply connected five-manifolds of Barden contains a simple topological description of the Wu manifold. The Wu manifold decomposes into two copies of the (unique) orientable non-trivial …
- 10.5k
3
votes
Can triangulations (or some related combinatorial structure) distinguish smooth structures o...
It is very hard to construct state-sum invariants that distinguish smooth structures in dimension 4, for this simple but crucial fact that is worth mentioning: if $M$ and $N$ are homeomorphic smooth 4 …
- 10.5k
9
votes
Accepted
Existence of fibered surfaces in arbitrary 4-manifolds?
I suppose that, for a $n$-manifold $M$, containing a "fibered codimension-2 manifold" $N\subset M$ means that $N$ has trivial normal neighbourhood $\nu N = N\times D^2$ and its complement $M \setminus …
- 10.5k
3
votes
Accepted
Geometry of a manifold after Dehn filling, in terms of geometry pre-filling
The general principle is that a generic filling of a geometric manifold belongs to the same geometry of the original manifold. This holds notably in hyperbolic geometry by Thurston's Dehn filling theo …
- 10.5k
5
votes
Accepted
Are Seifert fibered spaces with a horizontal surface exactly the surface bundles over the ci...
This is not quite true, because after splitting along the horizontal surface you may get interval bundles over non-orientable surfaces, and these are not products (I am assuming your 3-manifold is ori …
- 10.5k
3
votes
Accepted
Zero surgery on a Seifert fiber space
What you call a 0-surgery on a Seifert manifold is a move that typically does not produce a Seifert manifold. It is a move that "kills the fiber" and it produces a graph manifold, homeomorphic to a co …
- 10.5k
3
votes
Non-collapsible complexes
If you either collapse or de-collapse (the term expand is used here) a 2-dimensional polyhedron that contains a Bing's house, using only strata of dimension <=2, you end up with another 2-dimensiona …
- 10.5k