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Comparing combinatorial models of moduli space and their compactifications

Daniela Egas Santander and Alexander Kupers

Algebraic & Geometric Topology 24 (2024) 595–654
Abstract

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.

Keywords
moduli space, string topology, field theories
Mathematical Subject Classification 2010
Primary: 32G15, 57M15
Secondary: 57R56
References
Publication
Received: 5 October 2015
Revised: 18 July 2022
Accepted: 10 August 2022
Published: 12 April 2024
Authors
Daniela Egas Santander
Mathematical Institute
University of Bonn
Bonn
Germany
Alexander Kupers
Department of Mathematics
University of Toronto
Toronto, ON
Canada

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