A unique decomposition theorem for tight contact 3-manifolds

TL;DR

This paper proves that the prime summands in the unique decomposition of tight contact 3-manifolds are uniquely determined up to order and contactomorphism, strengthening the understanding of their structure.

Contribution

It establishes the uniqueness of the prime decomposition of tight contact 3-manifolds up to order and contactomorphism, building on Colin's earlier decomposition result.

Findings

Prime decomposition of tight contact 3-manifolds is unique.

Summands are determined up to order and contactomorphism.

Strengthens the structural understanding of tight contact 3-manifolds.

Abstract

It has been shown by V. Colin that every tight contact 3-manifold can be written as a connected sum of prime manifolds. Here we prove that the summands in this decomposition are unique up to order and contactomorphism.