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FANS AND LADDERS IN SMALL CANCELLATION THEORY

Published online by Cambridge University Press:  29 April 2002

JONATHAN P. McCAMMOND  and
DANIEL T. WISE
JONATHAN P. McCAMMOND
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. jon.mccammond@math.tamu.edu
DANIEL T. WISE
Affiliation:
Department of Mathematics, and Statistics, McGill University, Montreal, Quebec, Canada H3A 2K6. wise@math.mcgill.ca
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Abstract

This paper provides a strengthening of the theorems of small cancellation theory. It is proven that disc diagrams contain 'fans' of consecutive 2-cells along their boundaries. The size of these fans is linked to the strength of the small cancellation conditions satisfied by the diagram. A classification result is proven for disc diagrams satisfying small cancellation conditions. Any disc diagram either contains three fans along its boundary, or it is a ladder, or it is a wheel. Similar statements are proven for annular diagrams.

2000 Mathematical Subject Classification: 20F06.

Keywords

small cancellation theorydisc diagramfanladderwheel
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 84 , Issue 3 , May 2002 , pp. 599 - 644
Copyright
2002 London Mathematical Society

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