6
votes
2answers
714 views

Floer homology and Invariants for Einstein Field Equations?

Motivation: There have been the instanton (anti-self dual connection) solutions to the Yang-Mills equation $d_A^\ast F_A=0$ which extremize the YM energy $\int_M|F_A|^2$, leading to the Donaldson ...
4
votes
1answer
288 views

How to compute the Monopole Floer Homology for Surface $\times S^1$ ?

We know that Monopole Floer homology of a 3-manifold $M$ depends on a spin-c structure. My question is that if $M$ is $F\times S^1$ ($F$ is a surface of genus larger than 1) then how can we compute ...
11
votes
3answers
1k views

The “miracle” of Heegard Floer.

Taking tori in symmetric products and "miraculously" proving that the Floer homology is independent of choices always seemed, well, miraculous. Some time ago Max Lipyanski explained to me the origins ...