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Results tagged with gt.geometric-topology
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user 3634
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).
32
votes
Accepted
Suspension of a topological space
It’s not true. The Poincare sphere $P$ is a manifold, and its suspension is not. But its double suspension is homeomorphic to $S^5$ by Cannon’s “Double Suspension Theorem”. I learned about this from …
- 12.5k
2
votes
Is there a crossing-free planar embedding of the 2-skeleton of the 6-simplex?
Here is a positive answer using connected sets whose boundary is not a Jordan curve.
We want $m={n \choose k}$ connected sets, $S_1, S_2, \ldots , S_m\subseteq \mathbb{R}^2$. I'll want to associate …
- 12.5k
2
votes
A conjecture on antipodes and Jordan curves on the sphere
Let's say $C$ divides $S^2$ into two disks, $D$ and $E$. Then, choosing
a homeomorphism (fixing $C$) $h:D\to E$, we get an involution $t: S^2\to S^2$, which has degree $-1$. On the other hand, sinc …
- 12.5k
1
vote
"structure group" for fibration
My advisor (Sufian Husseini) wrote a book where something like this is done, based on the work in some of his first papers.
Husseini, S. Y.
The topology of classical groups and related topics. Gordon …
- 12.5k
13
votes
What is the intuition behind the Freudenthal suspension theorem?
The suspension map $\Sigma: [A, X] \to [\Sigma A, \Sigma X]$ (of which yours is a special case) is adjoint to a map $[A, X] \to [A, \Omega\Sigma X]$ which is induced by the map
$\sigma: X\to \Omega\S …
- 12.5k
33
votes
Accepted
Is every real n-manifold isomorphic to a quotient of $\mathbb{R}^n$?
Hahn–Mazurkiewicz Theorem: Suppose $X$ is a nonempty Hausdorff topological space.
Then the following are equivalent:
there is a surjection $[0,1]\to X$,
$X$ is compact, connected, locally connect …
- 12.5k