A semigroup of theta-curves in 3-manifolds

TL;DR

This paper proves an existence and uniqueness theorem for prime decompositions of theta-curves embedded in 3-manifolds, advancing the understanding of their structural properties.

Contribution

It introduces a new theorem establishing the existence and uniqueness of prime decompositions specifically for theta-curves in 3-manifolds.

Findings

Prime decompositions of theta-curves exist and are unique.

The theorem provides a foundational tool for studying theta-curves in topology.

Abstract

We establish an existence and uniqueness theorem for prime decompositions of theta-curves in $3$-manifolds.