2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73147We introduce a new invariant of bipartite chord diagrams and use it to construct the first examples of groups with Dehn function $n^2\log n$ and other small Dehn functions. Some of these groups have undecidable conjugacy problem.39 pages; We added a section where we prove that multiple HNN extensions of free groups having undecidable conjugacy problem cannot have Dehn functions smaller than n^2 log n; 9/14/05 - made changes suggested by the referee. The paper is accepted in GAFAGroup TheoryGeometric Topologytext