Meta-nilpotent quotients of mapping-torus groups and two topological invariants of quadratic forms

TL;DR

This paper investigates the structure of certain algebraic quotients of mapping-torus groups and introduces two quadratic form invariants for knots and mapping classes, linking algebraic properties to topological invariants.

Contribution

It determines the center of meta-nilpotent quotients of mapping-torus groups and introduces two new quadratic form invariants for knots and mapping classes.

Findings

Identified the center of specific algebraic quotients of mapping-torus groups.

Introduced two quadratic form invariants for knots and mapping classes.

Established a connection between algebraic structures and topological invariants.

Abstract

We determine the center of a meta-nilpotent quotient of a mapping-torus group. As a corollary, we introduce two invariants, which are quadratic forms, of knots and of mapping classes.