Moduli spaces of tropical curves of higher genus with marked points and homotopy colimits
| dc.creator | Kozlov, Dmitry N. | |
| dc.date | 2008-09-25 | |
| dc.date.accessioned | 2026-07-07T10:05:15Z | |
| dc.date.available | 2026-07-07T10:05:15Z | |
| dc.description | The 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.identifier | https://arxiv.org/abs/0809.4367 | |
| dc.identifier | http://arxiv.org/abs/0809.4367 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169958 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 57xx (Primary) 14Mxx, 55xx (Secondary) | |
| dc.title | Moduli spaces of tropical curves of higher genus with marked points and homotopy colimits | |
| dc.type | text |