We define the contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. More precisely, given a contact manifold $(M,\xi)$ and some auxiliary data $\mathcal{ D}$, we define an algebra $HC(\mathcal{ D})$. If $\mathcal{ D}_1$ and $\mathcal{ D}_2$ are two choices of auxiliary data for $(M,\xi)$, then $HC(\mathcal{ D}_1)$ and $HC(\mathcal{ D}_2)$ are isomorphic. We use a simplified version of Kuranishi perturbation theory, consisting of semi-global Kuranishi charts.
Categories: math.SG