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THE GALLERY LENGTH FILLING FUNCTION AND A GEOMETRIC INEQUALITY FOR FILLING LENGTH

Published online by Cambridge University Press:  18 April 2006

S. M. GERSTEN  and
T. R. RILEY
S. M. GERSTEN
Affiliation:
Department of Mathematics, 155S. 1400E., Room 233, University of Utah, Salt Lake City, UT 84112, USAgersten@math.utah.edu, www.math.utah.edu/~sg/
T. R. RILEY
Affiliation:
Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853-4201, USAtim.riley@math.cornell.edu, www.math.cornell.edu/~tim.riley/
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Abstract

We exploit duality considerations in the study of singular combinatorial 2-discs (diagrams) and are led to the following innovations concerning the geometry of the word problem for finite presentations of groups. We define a filling function called gallery length that measures the diameter of the 1-skeleton of the dual of diagrams; we show it to be a group invariant and we give upper bounds on the gallery length of combable groups. We use gallery length to give a new proof of the Double Exponential Theorem. Also we give geometric inequalities relating gallery length to the space-complexity filling function known as filling length.

Keywords

20F05 (primary)20F0657M0557M20 (secondary)
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 92 , Issue 3 , May 2006 , pp. 601 - 623
Copyright
2006 London Mathematical Society

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