The topology of moduli spaces of tropical curves with marked points
type: Item
instance of: scholarly article
title: The topology of moduli spaces of tropical curves with marked points
zbMATH Open document ID: 1193.14075
author: Dmitry N. Kozlov
published in: The Asian Journal of Mathematics
publication date: 2010-02-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/0809.4357
full work available at URL: https://projecteuclid.org/euclid.ajm/1261671495
review text: The author studies the topology of moduli spaces of tropical curves of genus \(g\) with \(n\) marked points. He considers the moduli spaces as being embedded in a larger space called the moduli space of metric graphs with \(n\) marked points, and he describes the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In particular, he studies the case \(g=1\) carefully and he shows that the corresponding moduli space is presented as a quotient space of torus with respect to the conjugation \(\mathbb Z_2\)-action. As its application, he also computes the all Betti numbers of \(\mathbb Z_2\) coefficients for this moduli space.
reviewed by: Kohhei Yamaguchi
Mathematics Subject Classification ID: 14T05
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 5665676
zbMATH Keywords: tropical geometry
zbMATH Keywords: combinatorial algebraic topology
zbMATH Keywords: complexes of trees
zbMATH Keywords: metric graph
MaRDI profile type: Publication
arXiv ID: 0809.4357
OpenAlex ID: W2964154731
DOI: 10.4310/AJM.2009.V13.N3.A8
description: scientific article