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Annular Dehn functions of groups

Published online by Cambridge University Press:  17 April 2009

Stephen G. Brick  and
Jon M. Corson
Stephen G. Brick
Affiliation:
Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, United States of America e-mail: brick@mathstat.usouthal.edu
Jon M. Corson
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa AL 35487-0350, United States of America e-mail: jcorson@mathdept.as.ua.edu
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Abstract

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For a finite presentation of a group, or more generally, a two-complex, we define a function analogous to the Dehn function that we call the annular Dehn function. This function measures the combinatorial area of maps of annuli into the complex as a function of the lengths of the boundary curves. A finitely presented group has solvable conjugacy problem if and only if its annular Dehn function is recursive.

As with standard Dehn functions, the annular Dehn function may change with change of presentation. We prove that the type of function obtained is preserved by change of presentation. Further we obtain upper bounds for the annular Dehn functions of free products and, more generally, amalgamations or HNN extensions over finite subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 453 - 464
Copyright
Copyright © Australian Mathematical Society 1998

References

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