Dehn functions of infinitely presented groups

Jeudi 12 juin 2008 14:00-15:00 - Grigorchuk Rostislav - Texas A&M University - IHES

Résumé : The talk is based on joint work with S.Ivanov.
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word problem for a group presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced functions (this equivalence fails for the standard Dehn function).
We also give upper bounds for these functions, as well as for the standard Dehn function, for two well-known periodic groups. In particular, we prove that the (standard) Dehn function of a 2-group $\Gamma$
of intermediate growth, defined by a system of defining relators due to Lysenok, is bounded from above by $C x2\log_2x$, where $C>1$ is a constant. We also show that the (standard) Dehn function of a free
$m$-generator Burnside group $B(m,n)$ of exponent $n \ge 2^48$, where
$n$ is either odd or divisible by $29$, defined by a minimal system of defining relators, is bounded from above by the subquadratic function
$x^19/12$.

Lieu : bât. 425 - 121-123

Dehn functions of infinitely presented groups  Version PDF