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Results tagged with 4-manifolds
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user 424
A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different.
6
votes
Compactify S^2\times S^2-\Delta
Any compactification of $S^2\times S^2\setminus\Delta$ which is simply connected and has the same homology as $S^2\times S^2$ will be at least homeomorphic to $S^2\times S^2$ (in particular it can't b …
- 2,927
13
votes
1
answer
1k
views
Gromov-Witten invariants counting curves passing through two points
Let us say that a closed symplectic manifold $X$ is $GW_g$-connected if there is a nonvanishing Gromov-Witten invariant of the form
$GW_{g,n}^{X,A}(\beta,point, point,\alpha_3,\ldots,\alpha_n)$ --in o …
- 2,927
7
votes
Accepted
Minimal genus, adjunction inequality
Regarding Question 2, Corollary 2 of this paper by Li shows that any symplectic four-manifold which contains a smoothly embedded homologically essential sphere with nonnegative intersection is obtaine …
- 2,927