Geodesic
Comparing combinatorial models of moduli space and their compactifications
Egas Santander, Daniela1 ; Kupers, Alexander2
1 Mathematical Institute, University of Bonn, Bonn, Germany
2 Department of Mathematics, University of Toronto, Toronto, ON, Canada
Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 595-654

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We compare two combinatorial models for the moduli space of two-dimensional cobordisms (namely Bödigheimer’s radial slit configurations and Godin’s admissible fat graphs), using a “critical graph” map to produce an explicit homotopy equivalence. 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.

DOI : 10.2140/agt.2024.24.595
Classification : 32G15, 57M15, 57R56
Keywords: moduli space, string topology, field theories

Egas Santander, Daniela 1 ; Kupers, Alexander 2

1 Mathematical Institute, University of Bonn, Bonn, Germany
2 Department of Mathematics, University of Toronto, Toronto, ON, Canada 
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Egas Santander, Daniela; Kupers, Alexander. Comparing combinatorial models of moduli space and their compactifications. Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 595-654. doi: 10.2140/agt.2024.24.595

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