Constructing convex planes in the pants complex
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- by Javier Aramayona, Hugo Parlier and Kenneth J. Shackleton
- Proc. Amer. Math. Soc. 137 (2009), 3523-3531
- DOI: https://doi.org/10.1090/S0002-9939-09-09907-9
- Published electronically: June 29, 2009
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Previous version: Original version posted May 15, 2009
Corrected version: Current version corrects publisher's omission of labels in Figure 2
Abstract:
Our main theorem identifies a class of totally geodesic subgraphs of the $1$-skeleton of the pants complex, referred to as the pants graph, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the pants graph of any surface of complexity at least $3$.References
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Bibliographic Information
- Javier Aramayona
- Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
- MR Author ID: 796736
- Email: Javier.Aramayona@nuigalway.ie
- Hugo Parlier
- Affiliation: Institute of Geometry, Algebra and Topology, École Polytechnique Fédérale de Lausanne, Bâtiment BCH, CH-1015 Lausanne, Switzerland
- MR Author ID: 767561
- Email: hugo.parlier@a3.epfl.ch
- Kenneth J. Shackleton
- Affiliation: University of Tokyo IPMU, 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8568, Japan
- Email: kenneth.shackleton@ipmu.jp, kjs2006@alumni.soton.ac.uk
- Received by editor(s): February 27, 2007
- Received by editor(s) in revised form: October 26, 2008
- Published electronically: June 29, 2009
- Additional Notes: The first author was partially supported by a short-term research fellowship at the Université de Provence, and the third author by a long-term JSPS postdoctoral fellowship, number P06034
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3523-3531
- MSC (2000): Primary 57M50; Secondary 05C12
- DOI: https://doi.org/10.1090/S0002-9939-09-09907-9
- MathSciNet review: 2515421