Search Results

Let $(\omega_t)_{t\in [0,1]}$ be a path of cohomologous symplectic forms on $X$. The standard Moser's argument shows that there exists a family of diffeomorphisms $(\psi_t)_{t\in [0,1]}$ of $X$ with $ …

Assume $(X,\omega)$ is a compact real $2n$-dimensional symplectic manifold with a Hamiltonian torus action corresponding to the moment map $\mu:X\to \mathfrak{t}^*\cong \mathbb{R}^k$. In this situati …

The symplectic sum of Gompf and the symplectic cut of Lerman are known to be inverse of each other, in the sense that if you apply one of these first and the other one afterward, you obtain the origin …

Blow-ups of points can also be performed in the symplectic category; for a given point $p\in (X,\omega)$ we choose a Darboux chart around $p$ and then use the symplectic cut corresponding to the stand …

Let $\psi_t: X\to X$, $t \in [0,1]$, be a path Hamiltonian diffeomorphism on a symplectic manifold $X$, given by functions $H_t$. If $H_t \equiv H$ is independent of $t$ then $$ \psi_1 = \psi_{\frac …

I got this answer from Dusa McDuff (and she got it from some body else): Suppose given $f:[0,1]\to [0,1]$ such thqt 0 is repelling fixed point and 1 is attracting fixed point and there are no others. …

Let $(X,\omega)$ be a symplectic 4-manifold such that $\omega$ has a rational cohomology class. I am interested in Donaldson divisors (surfaces) $D$ in $(X,\omega)$ whose complement is a 1-handle body …