Proceedings of the London Mathematical Society

Table of Contents - 2006 - Volume 92, Issue 03  


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

S. M. GERSTEN a1 and T. R. RILEY a2
a1 Department of Mathematics, 155S. 1400E., Room 233, University of Utah, Salt Lake City, UT 84112, USA gersten@math.utah.edu, www.math.utah.edu/~sg/
a2 Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853-4201, USA tim.riley@math.cornell.edu, www.math.cornell.edu/~tim.riley/

Article author query
gersten sm   [Google Scholar] 
riley tr   [Google Scholar] 
 

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.

(Published Online April 18 2006)
(Received October 10 2003)
(Revised June 3 2005)

Maths Classification

20F05 (primary); 20F06; 57M05; 57M20 (secondary).

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