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2 votes
0 answers
82 views

Why should we restrict the multiplicitiy of hyperbolic orbit to be one in Embedded contact homology?

Embedded contact homology(abbreviated by ECH) is a Floer type theory specially designed for three dimensional contanct manifolds(or generally, manifold with stable Hamiltonian structure) invented by ...
3 votes
0 answers
318 views

Bubbling off a sphere in a splitting/stretching manifold

This question is related to my old question Bubbling off of a pseudo holomorphic sphere on surface with cylindrical ends about the bubbling off argument in Seidel's paper The symplectic Floer homology ...
4 votes
2 answers
448 views

Dismissing pseudoholomorphic curves in embedded contact homology

In the papers The periodic Floer homology of a Dehn twist, Rounding corners of polygons and the embedded contact homology of $T^3$, and Combinatorial embedded contact homology for toric contact ...
4 votes
0 answers
385 views

Some clarifications on the PSS isomorphism in Hamiltonian Floer cohomology

I'm looking for some help in understanding the PSS isomorphism map in the context of Hamiltonian Floer cohomology and Morse cohomology with universal Novikov coefficients $\Lambda_{\omega}$ (à la ...
3 votes
0 answers
102 views

Continuation map interpolating two quadratic Hamiltonians with respect to different contact boundaries

Let $(M,\lambda)$ be a Liouville manifold. Consider two different contact boundaries $\partial_{\infty}^1M$ and $\partial_{\infty}^2M$ with respect to the same Liouville flow $Z$. Each of them ...
6 votes
1 answer
714 views

Bubbling off of a pseudo holomorphic sphere on surface with cylindrical ends

I need some clarification about the reason why we have a sphere bubbling off in the situation described by Seidel in The Symplectic Floer Homology of a Dehn Twist. I’ll try to summarize to the best ...
1 vote
1 answer
394 views

Floer equation and Cauchy Riemann equation

Consider a symplectic manifold $(M,\omega)$ with the property that $\pi_2(M) = 0$. Given a time dependent hamiltonian $H_t$ on $M$, and a $\omega$-compatible almost complex structure J on M, we may ...
11 votes
2 answers
444 views

Fredholm property about $L^p$-extension $(p\neq 2)$ of differential operators

The following is a well-known result for elliptic operators. Theorem. Let $P: \Gamma(E)\to \Gamma(F)$ be an elliptic operator of order $m$ between vector bundles $E$ and $F$ over a compact ...