Abstract
The idea of applying isoperimetric functions to group theory is due to M. Gromov [8], We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 515-523 |
| Number of pages | 9 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Volume | 36 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1993 |
| Externally published | Yes |
Keywords
- 05C25
- 1991 Mathematics subject classification
- 20F05
ASJC Scopus subject areas
- Mathematics(all)
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Huck, G., & Stephan Rosebrock, S. R. (1993). A bicombing that implies a sub-exponential isoperimetric inequality. Proceedings of the Edinburgh Mathematical Society, 36(3), 515-523. https://doi.org/10.1017/S0013091500018587