Groups with regular free length functions in Z^n
by
Denis Serbin
McGill University
Coauthors: Olga Kharlampovich, Alexei Myasnikov, Vladimir Remeslennikov

Finding description of finitely generated groups acting freely on Lambda-trees, or, equivalently groups having free length functions in Lambda (where Lambda is an ordered abelian group) is one of the major problems in Geometric Group Theory. This problem was solved for some special cases of Lambda but still is far from being solved in the general case. In my talk, at first, I'm going to introduce a natural restriction on length function which is called the regularity condition. Then I'm going to present the description of finitely generated groups with regular free length functions in Z^n, and to discuss why regularity condition is important.

Date received: February 26, 2006