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Spring 2010 Windmills and extreme $2$-cells
Jon McCammond, Daniel Wise
Illinois J. Math. 54(1): 69-87 (Spring 2010). DOI: 10.1215/ijm/1299679738

Abstract

In this article, we prove new results about the existence of $2$-cells in disc diagrams which are extreme in the sense that they are attached to the rest of the diagram along a small connected portion of their boundary cycle. In particular, we establish conditions on a $2$-complex $X$ which imply that all minimal area disc diagrams over $X$ with reduced boundary cycles have extreme $2$-cells in this sense. The existence of extreme $2$-cells in disc diagrams over these complexes leads to new results on coherence using the perimeter-reduction techniques we developed in an earlier article. Recall that a group is called coherent if all of its finitely generated subgroups are finitely presented. We illustrate this approach by showing that several classes of one-relator groups, small cancellation groups and groups with staggered presentations are collections of coherent groups.

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Jon McCammond. Daniel Wise. "Windmills and extreme $2$-cells." Illinois J. Math. 54 (1) 69 - 87, Spring 2010. https://doi.org/10.1215/ijm/1299679738

Information

Published: Spring 2010
First available in Project Euclid: 9 March 2011

zbMATH: 1238.57005
MathSciNet: MR2776985
Digital Object Identifier: 10.1215/ijm/1299679738

Subjects:
Primary: 20F06, 20F67, 57M07

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 1 • Spring 2010
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