Moduli spaces of metric graphs of genus 1 with marks on vertices

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dc.creatorKozlov, Dmitry N.
dc.date2008-09-25
dc.date.accessioned2026-07-07T10:05:15Z
dc.date.available2026-07-07T10:05:15Z
dc.descriptionIn this paper we study homotopy type of certain moduli spaces of metric graphs. More precisely, we show that the spaces $MG_{1,n}^v$, which parametrize the isometry classes of metric graphs of genus 1 with $n$ marks on vertices are homotopy equivalent to the spaces $TM_{1,n}$, which are the moduli spaces of tropical curves of genus 1 with $n$ marked points. Our proof proceeds by providing a sequence of explicit homotopies, with key role played by the so-called scanning homotopy. We conjecture that our result generalizes to the case of arbitrary genus.
dc.descriptionTopology and its Applications, In Press, Corrected Proof, Available online 3 August 2008
dc.identifierhttps://arxiv.org/abs/0809.4364
dc.identifierhttp://arxiv.org/abs/0809.4364
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169957
dc.subjectAlgebraic Topology
dc.subjectAlgebraic Geometry
dc.subject57xx (Primary) 14Mxx (Secondary)
dc.titleModuli spaces of metric graphs of genus 1 with marks on vertices
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