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 manifolds
Search options not deleted
user 23571
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
19
votes
Closed manifold with non-vanishing homotopy groups and vanishing homology groups
As suggested by Lennart Meier, the connected sum $M=P\#P$ of two copies of the Poincaré homology sphere gives an example. The homotopy groups $\pi_n(M)$ are nonzero for all $n>1$ because the universa …
- 19.4k
5
votes
Do $\mathbb{HP}^2\#\overline{\mathbb{HP}^2}$ and $\mathbb{OP}^2\#\overline{\mathbb{OP}^2}$ a...
Another way of describing the content of the previous answers is as follows. Suppose one starts with one of the Hopf bundles $p:S^{2n-1}\to S^n$ for $n=2,4,8$ coming from $\mathbb C$, $\mathbb H$, or …
- 20k
16
votes
Topological $n$-manifolds have the homotopy type of $n$-dimensional CW-complexes
This is a theorem on page 136 of Freedman and Quinn's book "Topology of 4-Manifolds", with a reference given to the Kirby-Siebenmann book for the higher-dimensional case. …
- 20k
7
votes
Inverse cohomological isomorphisms
In the reverse direction, any degree $1$ map $f:M\to N$ of closed connected orientable $n$-manifolds must induce a surjection on $\pi_1$, for otherwise $f$ could be lifted to the covering space $\tilde …
- 20k