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

作者：Kozlov Dmitry N^*

来源：Israel Journal of Mathematics, 2011, 182(1): 253-291.

DOI：10.1007/s11856-011-0031-7

The main characters of this paper are the moduli spaces TM (g,n) of tropical curves of genus g with n marked points, with g a parts per thousand yen 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 homotopy colimits of diagrams of topological spaces over combinatorially defined generalized simplicial complexes Delta (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.

• 出版日期2011-3