The periodic Floer homology of a Dehn twist.
Rounding corners of polygons and the embedded contact homology of .
The double bubble conjecture.
Circle-valued Morse theory and Reidemeister torsion.
An index inequality for embedded pseudoholomorphic curves in symplectizations
Let be a surface with a symplectic form, let be a symplectomorphism of , and let be the mapping torus of . We show that the dimensions of moduli spaces of embedded pseudoholomorphic curves in , with cylindrical ends asymptotic to periodic orbits of or multiple covers thereof, are bounded from above by an additive relative index. We deduce some compactness results for these moduli spaces. This paper establishes some of the foundations for a program with Michael Thaddeus, to understand...
Proof of the double bubble conjecture.
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