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Finite rigid subgraphs of pants graphs

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Abstract

Let \(S_{g,n}\) be an orientable surface of genus g with n punctures. We identify a finite rigid subgraph \(X_{g,n}\) of the pants graph \({\mathcal {P}}(S_{g,n})\), that is, a subgraph with the property that any simplicial embedding of \(X_{g,n}\) into any pants graph \({\mathcal {P}}(S_{g',n'})\) is induced by an embedding \(S_{g,n}\rightarrow S_{g',n'}\). This extends results of the third author for the case of genus zero surfaces.

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Acknowledgements

The authors would like to thank Javier Aramayona for useful conversations and the University of Warwick for its hospitality where this work began. The authors also thank the anonymous referee for helpful suggestions.

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Authors and Affiliations

  1. Universidad Nacional Autónoma de México, Centro de Ciencias Matemáticas, UNAM, Campus Morelia, 58190, Morelia, Mich, Mexico

    Jesús Hernández Hernández

  2. Department of Mathematics, Rice University, 6100 Main St., Houston, TX, 77005-1827, USA

    Christopher J. Leininger

  3. Walailak University, 222 Tumbon Thaiburi, Thasala, Nakhon Si Thammarat, 80160, Thailand

    Rasimate Maungchang

Authors
  1. Jesús Hernández Hernández
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  2. Christopher J. Leininger
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  3. Rasimate Maungchang
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Correspondence to Rasimate Maungchang.

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J. Hernández Hernández: Partially supported by the UNAM Post-Doctoral Scholarship Program 2017 at the CCMUNAM, the CNRSCONACYT UMI International Laboratory Solomon Lefschetz, the projects UNAM-PAPIIT IN102018, and UNAM-PAPIIT IA104620. C. J. Leininger: Partially supported by NSF Grant DMS-1811518 and NSF Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). R. Maungchang: Partially supported by The Coordinating Center for Thai Government Science and Technology Scholarship Students (CSTS), National Science and Technology Development Agency (NSTDA), Thailand (No. FDA-CO-2561-8553-TH)

Appendix: Additional examples of finite rigid sets

Appendix: Additional examples of finite rigid sets

Here we provide three additional examples of the finite rigid sets from Sect. 6 to better illustrate the construction.

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Hernández Hernández, J., Leininger, C.J. & Maungchang, R. Finite rigid subgraphs of pants graphs. Geom Dedicata 212, 205–223 (2021). https://doi.org/10.1007/s10711-020-00555-1

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  • DOI: https://doi.org/10.1007/s10711-020-00555-1

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