The Weinstein conjecture for connected sums

TL;DR

This paper proves the Weinstein conjecture for certain contact manifolds formed by connected sums, under specific topological conditions like non-trivial fundamental group or torsion-free homology.

Contribution

It establishes the Weinstein conjecture for connected sums of contact manifolds with particular topological properties, expanding the class of manifolds where the conjecture holds.

Findings

Proves the Weinstein conjecture for connected sums with non-trivial fundamental group.

Proves the Weinstein conjecture for connected sums with torsion-free homology.

Extends the scope of the Weinstein conjecture to new classes of contact manifolds.

Abstract

We prove the Weinstein conjecture for non-trivial contact connected sums under either of two topological conditions: non-trivial fundamental group or torsion-free homology.