A QUASI-ISOMETRY INVARIANT LOOP SHORTENING PROPERTY FOR GROUPS
2008 ◽
Vol 18
(08)
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pp. 1243-1257
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Keyword(s):
We first introduce a loop shortening property for metric spaces, generalizing the property considered by M. Elder on Cayley graphs of finitely generated groups. Then using this metric property, we define a very broad loop shortening property for finitely generated groups. Our definition includes Elder's groups, and unlike his definition, our property is obviously a quasi-isometry invariant of the group. Furthermore, all finitely generated groups satisfying this general loop shortening property are also finitely presented and satisfy a quadratic isoperimetric inequality. Every CAT(0) cubical group is shown to have this general loop shortening property.
2012 ◽
Vol 22
(06)
◽
pp. 1250050
2018 ◽
Vol 98
(3)
◽
pp. 422-433
2005 ◽
Vol 134
(1)
◽
pp. 289-294
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1992 ◽
Vol 45
(3)
◽
pp. 513-520
◽
2014 ◽
Vol 24
(06)
◽
pp. 909-922
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Keyword(s):