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

DOI:
https://doi.org/10.1090/S0002-9939-09-09907-9

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 -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 .

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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:
https://doi.org/10.1090/S0002-9939-09-09907-9

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.