## New answers tagged 4-manifolds

0

I think the topological case is handled by this:
Brown, Morton
A mapping theorem for untriangulated manifolds. 1962 Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) pp. 92–94
According to the review on MathSciNet, it shows that an $n$-manifold $M$ has the form $M = X \cup_\alpha D^m$ where $\dim(X) < n$. I don't ...

8

For the smooth case:
Via Morse theory the claim is equivalent to having a Morse function with only one maximum, or only one minimum, or to have a handle decomposition with only one 0-handle.
Assume you have several 0-handles. By connectedness they have to be connected via 1-handles. Smale's handle cancellation says that a k-handle can be canceled against a ...

2

This is not Taubes' moduli space. Taubes has many more constraints on the currents, so that his "moduli space" is really a finite set of points (for generic $J$), and he requires special weightings on the multiply-covered curves (which are necessarily unbranched covers of tori due to his constraints) to get a well-defined count from his set of currents. He ...

Top 50 recent answers are included