Twisted Lefschetz number and Nielsen number
Haimiao Chen

TL;DR
This paper explores the twisted Lefschetz number, providing a homology-based formula, and introduces a method to estimate the Nielsen number, including an algorithm for abelian fundamental groups and a proof related to Bass' conjecture.
Contribution
It presents a new formula for the twisted Lefschetz number and a novel approach to estimate the Nielsen number, with applications to algorithms and group theory conjectures.
Findings
Derived a homology formula for the twisted Lefschetz number
Proposed a method to estimate the Nielsen number
Developed an algorithm for spaces with abelian fundamental groups and proved Bass' conjecture for certain groups
Abstract
We study the twisted Lefschetz number, which is a generalization of classical Lefschetz number. A formula in terms of homology with local coefficients is given. We then propose a method to estimate the Nielsen number. As applications, an algorithm for computing the Nielsen number of a self map of a space with abelian fundamental group is discussed; and Bass' conjecture for a class of groups is proved.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis · Geometric and Algebraic Topology
