Sheaf Theoretic Approach to Lefschetz Calculus

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arxiv 2410.13653 v2 pith:7VRALEOO submitted 2024-10-17 math.AT

Alejandro O. Majadas-Moure , David Mosquera-Lois This is my paper · ORCID

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keywords invariantlefschetzspacesalgebraicapproachcalculusdatalift

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

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A Combinatorial Study of the Fixed Point Index
math.AT 2025-05 reject novelty 5.0 of 10

The paper defines a combinatorial fixed point index as the classical index of the interior of a subspace, and develops integration theory with respect to it, generalizing the combinatorial Lefschetz number.