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Deep pockets in lattices and other groups
Author(s):
Andrew
D.
Warshall
Journal:
Trans. Amer. Math. Soc.
362
(2010),
577-601.
MSC (2000):
Primary 20F65
Posted:
September 17, 2009
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Abstract:
We show the nonexistence of deep pockets in a large class of groups, extending a result of Bogopol'skiĭ. We then give examples of important groups (namely lattices in Nil and Sol) which have deep pockets.
References:
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- 6.
- Jörg Lehnert, Some remarks on depth of dead ends in groups, available from the arXiv at math.GR/0703636, 2007.
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- Tim R. Riley and Andrew D. Warshall, The unbounded dead-end depth property is not a group invariant, Internat. J. Algebra Comput. 16 (2006), no. 5, 969-83. MR 2274725 (2007h:20040)
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- William Thurston, Three-dimensional geometry and topology, Princeton Mathematical Series, vol. 35, Princeton University Press, Princeton, 1997. MR 1435975 (97m:57016)
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Additional Information:
Andrew
D.
Warshall
Affiliation:
Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
Email:
andrew.warshall@yale.edu
DOI:
10.1090/S0002-9947-09-04954-X
PII:
S 0002-9947(09)04954-X
Received by editor(s):
March 30, 2007
Posted:
September 17, 2009
Additional Notes:
The author thanks his advisor, Andrew Casson, as well as John Mackay and Joshua Zelinsky for their helpful comments and the anonymous referee for two careful readings.
Copyright of article:
Copyright
2009,
Andrew D. Warshall
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