Sheaf Theoretic Approach to Lefschetz Calculus

TL;DR

This paper introduces a sheaf theoretic framework to extend the Lefschetz number from a classical algebraic invariant to a more general invariant applicable to morphisms of data over topological spaces.

Contribution

It presents a novel sheaf theoretic approach to Lefschetz calculus, broadening its applicability to data morphisms.

Findings

Extended Lefschetz number as a sheaf invariant

Applicable to morphisms of data over spaces

Provides new tools for topological data analysis

Abstract

We lift the Lefschetz number from an algebraic invariant of maps between spaces to an invariant of morphisms of data over the spaces.