Heegaard genus, cut number, weak p-congruence, and quantum invariants

TL;DR

This paper introduces a new quantum invariant for 3-manifolds, j_p, which relates to classical topological measures and remains invariant under weak p-congruence, enhancing understanding of 3-manifold classification.

Contribution

It defines the invariant j_p using quantum invariants and establishes its relation to Heegaard genus, cut number, and weak p-congruence invariance.

Findings

j_p is a non-negative integer invariant of 3-manifolds.

j_p relates to Heegaard genus and cut number.

j_p remains invariant under weak p-congruence.

Abstract

We use quantum invariants to define a 3-manifold invariant j_p which lies in the non-negative integers. We relate j_p to the Heegard genus, and the cut number. We show that j_$ is an invariant of weak p-congruence.