On the principal ideal theorem in arithmetic topology

TL;DR

This paper establishes an analogue of the principal ideal theorem within the context of arithmetic topology, relating algebraic number theory concepts to 3-manifolds.

Contribution

It introduces a novel theorem connecting principal ideals to 3-manifolds, extending classical algebraic number theory results into topology.

Findings

Proves the principal ideal theorem analogue for 3-manifolds

Bridges concepts between algebraic number theory and topology

Provides new insights into the structure of 3-manifolds

Abstract

In this paper we state and prove the analogous of the principal ideal theorem of algebraic number theory for the case of 3-manifolds from the point of view of arithmetic topology.