Super-exponential 2-dimensional Dehn functions

Super-exponential 2-dimensional Dehn Functions

We produce examples of groups of type F3 with 2–dimensional Dehn functions of the form exp(x) (a tower of exponentials of height n), where n is any natural number.

The Mean Dehn Functions of Abelian Groups

While Dehn functions, D(n), of finitely presented groups are very well studied in the literature, mean Dehn functions are much less considered. M. Gromov introduced the notion of mean Dehn function of a group, Dmean(n), suggesting that in many cases it should grow much more slowly than the Dehn function itself. Using only elementary counting methods, this paper presents some computations pointi...

Homological Dehn Functions and the Word Problem

S. M. Gersten Abstract. Homological Dehn functions over R and over Z are introduced to measure minimal fillings of integral 1-cycles by (real or integral) 2-chains in the Cayley 2complex of a finitely presented group. If the group G is the fundamental group of a finite graph of finitely presented vertex-groups Hv and finitely generated edge-groups, then there is a formula for an isoperimetric f...

Groups with Quadratic-Non-Quadratic Dehn Functions

We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.

Dehn Functions and Non-Positive Curvature