The gallery length filling function and a geometric inequality for filling length

• Autores: S.M. Gersten, T.R. Riley
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 92, Nº 3, 2006, págs. 601-623
• Idioma: inglés
• DOI: 10.1017/s0024611505015649
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• Resumen

  • 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.