On Dehn functions and products of groups

Brick, Stephen G.

doi:10.1090/S0002-9947-1993-1102884-1

On Dehn functions and products of groups
HTML articles powered by AMS MathViewer

by Stephen G. Brick PDF

Trans. Amer. Math. Soc. 335 (1993), 369-384 Request permission

Abstract:

If $G$ is a finitely presented group then its Dehn function—or its isoperimetric inequality—is of interest. For example, $G$ satisfies a linear isoperimetric inequality iff $G$ is negatively curved (or hyperbolic in the sense of Gromov). Also, if $G$ possesses an automatic structure then $G$ satisfies a quadratic isoperimetric inequality. We investigate the effect of certain natural operations on the Dehn function. We consider direct products, taking subgroups of finite index, free products, amalgamations, and $\text {HNN}$ extensions.

References

Juan M. Alonso, Inégalités isopérimétriques et quasi-isométries, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 12, 761–764 (French, with English summary). MR 1082628

Sur les groupes hyperboliques d’après Mikhael Gromov

G. Baumslag, S. M. Gersten, M. Shapiro, and H. Short, Automatic groups and amalgams, J. Pure Appl. Algebra 76 (1991), no. 3, 229–316. MR 1147304, DOI 10.1016/0022-4049(91)90139-S
Stephen G. Brick, Dehn functions of groups and extensions of complexes, Pacific J. Math. 161 (1993), no. 1, 115–127. MR 1237140
M. Coornaert, T. Delzant, and A. Papadopoulos, Géométrie et théorie des groupes, Lecture Notes in Mathematics, vol. 1441, Springer-Verlag, Berlin, 1990 (French). Les groupes hyperboliques de Gromov. [Gromov hyperbolic groups]; With an English summary. MR 1075994
David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Michael S. Paterson, and William P. Thurston, Word processing in groups, Jones and Bartlett Publishers, Boston, MA, 1992. MR 1161694

Dehn functions and

norms of finite presentations

M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}

Regular subgroups of automatic groups