  The goal of this paper is to set up the general framework of
higher-dimensional Heegaard Floer homology, define the contact class, and use
it to give an obstruction to the Liouville fillability of a contact manifold
and a sufficient condition for the Weinstein conjecture to hold. We discuss
several classes of examples including those coming from analyzing a close
cousin of symplectic Khovanov homology and the analog of the Plamenevskaya
invariant of transverse links.
