Exotic tight contact structures on $\mathbb{R}^n$

TL;DR

This paper introduces a new contact homology variant for convex open contact manifolds and demonstrates the existence of infinitely many exotic tight contact structures on Euclidean spaces of dimension greater than three.

Contribution

It develops a novel contact homology framework and proves the existence of numerous exotic tight contact structures on high-dimensional Euclidean spaces.

Findings

Existence of infinitely many exotic tight contact structures on $\

Development of a new contact homology variant for convex open contact manifolds.

Abstract

We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.