Minimal fixed point set of maps on Torus Fiber Bundles over the Circle

TL;DR

This paper investigates the minimal fixed point sets of fiber-preserving maps on torus fiber bundles over the circle, utilizing one-parameter fixed point theory to relate these sets to algebraic properties of the fundamental group.

Contribution

It introduces a method to describe minimal fixed point sets in fiber bundles over the circle with torus fibers using algebraic topological tools.

Findings

Characterization of fixed point sets via fundamental group homomorphisms

Application of one-parameter fixed point theory to fiber bundles

Explicit descriptions of fixed point sets in specific cases

Abstract

The main purpose this work is to study the minimal fixed point set of fiber-preserving maps for spaces which are fiber bundles over the circle and the fiber is the torus. Using the one-parameter fixed point theory is possible to describe these sets in terms of the fundamental group and the induced homomorphism.