On Dehn Functions of Amalgamations and Strongly Undistorted Subgroups

We study the Dehn functions of amalgamations, introducing the notion of strongly undistorted subgroups. Using this, we give conditions under which taking an amalgamation does not increase the Dehn function, generalizing one aspect of the combination theorem of Bestvina and Feighn. To obtain examples of strongly undistorted subgroups, we define and study the relative Dehn function of pairs of groups. As a result we obtain a new method of constructing examples of pairs of groups that are relatively hyperbolic in the sense of Farb.

• Type: Journal
• Year: 2000
• Where: IJAC
• Authors: Stephen G. Brick, Jon M. Corson
• Keywords: Dehn Function, IJAC 2000, Relative Dehn Function, Undistorted Subgroups