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An l1-norm function is introduced as a computational tool to estimate the Dehn function of a finite presentation and settle certain imbedding questions for finitely presented groups.

- S. M. Gersten
- 2001

We survey current work relating to isoperimetric functions and isodiametric functions of finite presentations. §

- S. M. Gersten, T. R. Riley
- 2000

Filling length measures the length of the contracting closed loops in a null-homotopy. The filling length function of Gromov for a finitely presented group measures the filling length as a function of length of edge-loops in the Cayley 2-complex. We give a bound on the filling length function in terms of the log of an isoperimetric function multiplied by a… (More)

- S. M. Gersten
- 1996

If K = Goφ Z where φ is a tame automorphism of the 1-relator group G, then the combinatorial area of loops in a Cayley graph of G is undistorted in a Cayley graph of K. Examples of distortion of area in fibres of fibrations over the circle are given and a notion of exponent of area distortion is introduced and studied. The inclusion of a finitely generated… (More)

- S. M. Gersten
- IJAC
- 1992

- BY S. M. GERSTEN, J. H. C. Whitehead, S. M. Gersten
- 2007

One can decide effectively when two finitely generated subgroups of a finitely generated free group F are equivalent under an automorphism of F. The subgroup of automorphisms of F mapping a given finitely generated subgroup S of F into a conjugate of S is finitely presented. In two famous articles [9, 10] which appeared in 1936, J. H. C. Whitehead, using… (More)

- S. M. Gersten
- 2005

We exploit duality considerations in the study of singular combinatorial 2-discs (diagrams) and are led to the following innovations concerning the geometry of the word problem for finite presentations of groups. We define a filling function called gallery length that measures the diameter of the 1-skeleton of the dual of diagrams; we show it to be a group… (More)

- S. M. Gersten
- IJAC
- 1991

The relevant definitions of terms occurring in the statement are as follows. If P = 〈x1, x2, . . . , xp | R1, R2, . . .Rq〉 is a finite presentation, we shall denote by G = G(P) the associated group; here G = F/N , where F is the free group freely generated by the generators x1, . . . , xp and N is the normal closure of the relators. If w is an element of F… (More)

- S. M. Gersten
- 1995

If the finitely presented group G splits over the finitely presented subgroup C, then classes are constructed in H2 (∞) (G) which reflect the splitting and which serve as lower bounds for isoperimetric functions for G. It is proved that H2 (∞) (G) = 0 for all word hyperbolic groups G. A converse is obtained for the combination theorem for hyperbolic groups… (More)

- S. M. Gersten
- 2003

We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we give innovations in the following two topics in Geometric Group Theory, where the conjectures have applications. (i.) Central Extensions. We describe an electrostatic model concerning how van Kampen diagrams change when one takes a central… (More)