TL;DR
This paper introduces a new chain complex based on semistable ribbon graphs, extending Kontsevich's graph homology by utilizing orbicell decomposition of the Deligne-Mumford compactification.
Contribution
It develops a novel semistable graph homology framework using orbicell decomposition, expanding the scope of Kontsevich's original graph homology.
Findings
Constructed a chain complex from semistable ribbon graphs.
Extended Kontsevich's graph homology to include semistable cases.
Linked orbicell decomposition with graph homology.
Abstract
Using the orbicell decomposition of the Deligne-Mumford compactification of the moduli space of Riemann surfaces studied previously, a chain complex based on semistable ribbon graphs is constructed which is an extension of Konsevich's graph homology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Topological and Geometric Data Analysis