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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 ...
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 ...
2 votes
0 answers
115 views

Higher genus (Hamiltonian perturbed) holomorphic curves in cotangent bundle of S^1

Consider $T^*S^1$ as symplectic manifold, with hamiltonian function $H(x,y) = y^2$ (y is the fiber direction, I know this is morse bott but it can be perturbed). consider the set of maps $u: \Sigma \...
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 ...
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 ...
6 votes
1 answer
741 views

Intuition about bubbling off a ghost bubble

I'm trying to improve my intuition about the bubbling phenomenon for $J$-holomorphic curves $\Sigma \to (M,\omega)$, where $\Sigma$ is a compact Riemann surface with possibly boundary. I assume that ...