Geometric & Functional Analysis GAFA

, Volume 16, Issue 6, pp 1324–1376

Groups with small Dehn functions and bipartite chord diagrams


DOI: 10.1007/s00039-006-0580-9

Cite this article as:
Ol’shanskii, A.Y. & Sapir, M.V. GAFA, Geom. funct. anal. (2006) 16: 1324. doi:10.1007/s00039-006-0580-9


We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n2log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show that n2log n is the smallest Dehn function of a multiple HNN extension of a free group with undecidable conjugacy problem.

Keywords and phrases.

Dehn function conjugacy problem S-machine chord diagram 

AMS Mathematics Subject Classification.

20E07 20F06 20F10 

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA
  2. 2.Department of Higher Algebra, MEHMATMoscow State UniversityMoscowRussia

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