Comparing combinatorial models of moduli space and their compactifications
arXiv:1506.02725 · doi:10.2140/agt.2024.24.595
Abstract
We compare two combinatorial models for the moduli space of two-dimensional cobordisms: Bödigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. We also discuss natural compactifications of these two models, the unilevel harmonic compactification and Sullivan diagrams respectively, and prove that the homotopy equivalence induces a cellular homeomorphism between these compactifications.
47 pages, 23 figures. Final version
References in corpus (5)
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- Natural operations on the Hochschild complex of commutative Frobenius algebras via the complex of looped diagrams
- Comparing fat graph models of moduli space
- The complex of formal operations on the Hochschild chains of commutative algebras
- Homology of the mapping class group for surfaces of genus 2 with boundary