Moduli spaces of tropical curves of higher genus with marked points and homotopy colimits

dc.creatorKozlov, Dmitry N.
dc.date2008-09-25
dc.date.accessioned2026-07-07T10:05:15Z
dc.date.available2026-07-07T10:05:15Z
dc.descriptionThe main characters of this paper are the moduli spaces $TM_{g,n}$ of rational tropical curves of genus $g$ with $n$ marked points, with $g\geq 2$. We reduce the study of the homotopy type of these spaces to the analysis of compact spaces $X_{g,n}$, which in turn possess natural representations as a homotopy colimits of diagrams of topological spaces over combinatorially defined generalized simplicial complexes $Δ_g$, with the latter being interesting on their own right. We use these homotopy colimit representations to describe a CW complex decomposition for each $X_{g,n}$. Furthermore, we use these developments, coupled with some standard tools for working with homotopy colimits, to perform an in-depth analysis of special cases of genus 2 and 3, gaining a complete understanding of the moduli spaces $X_{2,0}$, $X_{2,1}$, $X_{2,2}$, and $X_{3,0}$, as well as a partial understanding of other cases, resulting in several open questions and in further conjectures.
dc.identifierhttps://arxiv.org/abs/0809.4367
dc.identifierhttp://arxiv.org/abs/0809.4367
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169958
dc.subjectAlgebraic Topology
dc.subjectAlgebraic Geometry
dc.subject57xx (Primary) 14Mxx, 55xx (Secondary)
dc.titleModuli spaces of tropical curves of higher genus with marked points and homotopy colimits
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