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disc diagram

Proceedings of the London Mathematical Society (1)

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FANS AND LADDERS IN SMALL CANCELLATION THEORY
JONATHAN P. McCAMMOND, DANIEL T. WISE
Journal:

Proceedings of the London Mathematical Society / Volume 84 / Issue 3 / May 2002

Published online by Cambridge University Press:

29 April 2002, pp. 599-644

Print publication:

May 2002
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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.