An algebraic generalization of Giroux's criterion

Abstract

We compute the contact homology algebra of a neighborhood $({\mathbb{R}}_{\tau }\times W,\xi )$ of a convex hypersurface $W$ of any even dimension. This algebra is the derived tensor product of the augmentations of the chain-level contact homology of the dividing set, determined by the positive and negative regions of $W$. We describe methods for determining when the contact homology of $({\mathbb{R}}_{\tau }\times W,\xi )$ is non-zero in certain cases, which can be used to infer tightness of $\xi$. Full computations of contact homology are carried out in the case $\dim W=2$.

arXiv comment111 pages, 12 figures. v4: Corrected algebraic statements, new results on admissible sequences of contact forms, various typo corrections