Work

Tropical moduli spaces as symmetric Δ$\Delta$‐complexes

Year: 2022

Type: article

Abstract: We develop techniques for studying fundamental groups and integral singular homology of symmetric Δ $\Delta$ -complexes, and apply these techniques to study moduli spaces of stable tropical curves of unit volume, with and without marked points. As one application, we show that Δ g $\Delta _g$ and Δ g , n $\Delta _{g,n}$ are simply connected, for g ⩾ 1 $g \geqslant 1$ . We also show that Δ 3 $\Delta _3$ is homotopy equivalent to the 5-sphere, and that Δ 4 $\Delta _4$ has 3-torsion in H 5 $H_5$ .

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.12570

Authors: Daniel Allcock, Daniel Corey, Sam Payne

Institutions: The University of Texas at Austin, Technische Universität Berlin

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Awards: FRG: Collaborative Research: Matroids, Graphs, and Algebraic Geometry, RTG: Algebraic Geometry, Applied Algebra, and Number Theory at the University of Wisconsin, Tropical and nonarchimedean analytic methods in algebraic geometry, G4797137592