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Results tagged with at.algebraic-topology
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user 50754
Homotopy theory, homological algebra, algebraic treatments of manifolds.
15
votes
Simply-connected rational homology spheres
Yes, every simply-connected rational homology $4$-sphere is topologically the $4$-sphere. Simply-connected closed topological $4$-manifolds are classified by their intersection form $Q_X:H^2(X;\Bbb Z …
- 773
5
votes
1
answer
230
views
$\pi_1$ of 4-manifolds that "look like" disk bundles
Let $X$ be a smooth compact oriented 4-manifold with $\partial X=L(p,1)$, $H_2(X;\Bbb Z)=\Bbb Z$, $H_3(X; \Bbb Z)=0$ and the induced map $\pi_1(L(p,1)) \to X$ surjective. What are the possibilities fo …
- 773
17
votes
Theorems that led to very successful research programs in Geometry and Topology
In 1982, Richard Hamilton proved that a smooth closed 3-manifold admitting a metric with strictly positive Ricci curvature is a spherical space form (in particular such a manifold which is simply conn …
3
votes
Is $TS^n$ diffeomorphic to an open subset of $\mathbb{R}^{2n}$
There are no sphere's with non-trivial normal bundle in that dimension. As far as I know, this is originally a theorem of Massey. See http://www.ams.org/journals/proc/1959-010-06/S0002-9939-1959-0109 …
- 773