Filling length in finitely presentable groups. Dedicated to John Stallings on the occasion of his 65th birthday

SM Gersten, TR Riley

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We study the filling length function for a finite presentation of a group Gamma, and interpret this function as an optimal bound on the length of the boundary loop as a vanKampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of Gamma. We look at 'AD-pairs' (f,g) for a finite presentation cal P: that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for cal P. Further we show that (up to multiplicative constants) if x(r) is an isoperimetric function (r greater than or equal to 2) for a finite presentation then (x(r),x(r-1)) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.
Translated title of the contributionFilling length in finitely presentable groups. Dedicated to John Stallings on the occasion of his 65th birthday
Original languageEnglish
Pages (from-to)41 - 58
Number of pages18
JournalGeometriae Dedicata
Volume92
Publication statusPublished - 2002

Bibliographical note

Publisher: Kluwer Academic Publ

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