On the tropical Lefschetz-Hopf trace formula
Johannes Rau
TL;DR
This paper establishes a tropical Lefschetz-Hopf trace formula for matroidal automorphisms, linking fixed flats' beta invariants to the trace formula in tropical geometry.
Contribution
It introduces a novel tropical Lefschetz-Hopf trace formula specifically for matroid automorphisms, connecting combinatorial invariants to tropical fixed point theory.
Findings
Both sides of the formula equal the beta invariant of fixed flats.
The formula generalizes classical Lefschetz-Hopf results to tropical and matroidal settings.
Provides a new tool for studying automorphisms in tropical geometry.
Abstract
In this follow-up to arXiv:2007.11642, our main result is a tropical Lefschetz-Hopf trace formula for matroidal automorphisms. We show that both sides of the formula are equal to the (generalized) beta invariant of the lattice of fixed flats.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons · Advanced Algebra and Geometry