Stein domains with exotic contact boundaries

Abstract

We introduce a new invariant, the \textit{positive idempotent group}, for strongly asymptotically dynamically convex contact manifolds. This invariant can be used to distinguish different contact structures. As an application, for any complex dimension $n>8$ and any positive integer $k$, we can construct $n-$dimensional Stein manifolds $V_0,V_1,\cdots ,V_k$ such that ${\tilde{H}}_j(V_i)=0,j\ne n-1,n$, $V_i^{\prime }s$ are almost symplectomorphic, their boundaries are in the same almost contact class but not contactomorphic.

53 pages, 5 figures

References in corpus (1)

• Functors and Computations in Floer homology with Applications Part II