Comparing combinatorial models of moduli space and their compactifications

Egas Santander, Daniela; Kupers, Alexander

doi:10.2140/agt.2024.24.595

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Comparing combinatorial models of moduli space and their compactifications

Daniela Egas Santander and Alexander Kupers

Algebraic & Geometric Topology 24 (2024) 595–654

DOI: 10.2140/agt.2024.24.595

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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 2 (2024)