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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Constructing convex planes in the pants complex


Authors: Javier Aramayona, Hugo Parlier and Kenneth J. Shackleton
Journal: Proc. Amer. Math. Soc. 137 (2009), 3523-3531
MSC (2000): Primary 57M50; Secondary 05C12
Published electronically: June 29, 2009
Previous version: Original version posted May 15, 2009
Corrected version: Current version corrects publisher's omission of labels in Figure 2
MathSciNet review: 2515421
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Abstract | References | Similar Articles | Additional Information

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$.


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Additional Information

Javier Aramayona
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
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
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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09907-9
PII: S 0002-9939(09)09907-9
Keywords: Pants complex, Weil-Petersson metric
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.