Compactifications of Moduli Spaces and Cellular Decompositions

TL;DR

This paper investigates the topological structure of compactified moduli spaces of Riemann surfaces and introduces orbicell decompositions using semistable ribbon graphs, extending previous work.

Contribution

It identifies the homeomorphism types of certain compactifications and develops orbicell decompositions based on semistable ribbon graphs.

Findings

Homeomorphism types of compactified moduli spaces determined

Orbifold cell decompositions constructed using semistable ribbon graphs

Extension of Looijenga's work on cell decompositions

Abstract

This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier work of Looijenga.