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

SM Gersten, TR Riley

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

2 Citations (Scopus)

Abstract

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.
Translated title of the contributionThe gallery length filling function and a geometric inequality for filling length
Original languageEnglish
Pages (from-to)601 - 623
Number of pages23
JournalProceedings of the London Mathematical Society
Volume92(3)
DOIs
Publication statusPublished - May 2006

Bibliographical note

Publisher: Cambridge University Press

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