Geometric & Functional Analysis GAFA

, Volume 16, Issue 6, pp 1324-1376

First online:

Groups with small Dehn functions and bipartite chord diagrams

  • Alexander Yu. Ol’shanskiiAffiliated withDepartment of Mathematics, Vanderbilt UniversityDepartment of Higher Algebra, MEHMAT, Moscow State University Email author 
  • , Mark V. SapirAffiliated withDepartment of Mathematics, Vanderbilt University

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We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function n 2log n. Some of these groups have undecidable conjugacy problem. Our groups are multiple HNN extensions of free groups. We show that n 2log 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