Topology of the tropical moduli spaces \(\Delta_{2,n}\)
type: Item
instance of: scholarly article
title: Topology of the tropical moduli spaces \(\Delta_{2,n}\)
zbMATH Open document ID: 1505.14130
author: Melody Chan
published in: Beiträge zur Algebra und Geometrie
publication date: 2022-03-22T00:00:00Z
review text: Isomorphism classes of tropical curves are naturally parametrized by a tropical moduli space \(M_{g,n}^{\mathrm{trop}}\), in analogy with classical complex curves. As a generalized cone complex, this space is contractible, however its link \(\Delta_{g,n}\) is topologically nontrivial, and it actually coincides with the boundary complex of the Deligne-Mumford compactification of \(M_{g,n}\). In this paper, the author proves that \(\Delta_{2,n}\) is \(n\)-connected and computes the two top \(\mathbb{Q}\)-cohomology groups for \(n\) up to \(8\). These result fit into a series of recent papers by the author and others on the topology of \(M_{g,n}\), such as [\textit{M. Chan} et al., J. Am. Math. Soc. 34, No. 2, 565--594 (2021; Zbl 1485.14045)].
reviewed by: Daniele Agostini
Mathematics Subject Classification ID: 14T20
Mathematics Subject Classification ID: 14H10
zbMATH DE Number: 7495602
zbMATH Keywords: tropical geometry
zbMATH Keywords: tropical curves
zbMATH Keywords: moduli spaces
describes a project that uses: SageMath
MaRDI profile type: Publication
full work available at URL: s13366-021-00563-6
OpenAlex ID: W3130706411
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DOI: 10.1007/S13366-021-00563-6
description: scientific article; zbMATH DE number 7495602