ROAD TRIPS IN GEODESIC METRIC SPACES AND GROUPS WITH QUADRATIC ISOPERIMETRIC INEQUALITIES
2012 ◽
Vol 22
(06)
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pp. 1250050
Keyword(s):
The Road
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We introduce a property of geodesic metric spaces, called the road trip property, that generalizes hyperbolic and convex metric spaces. This property is shown to be invariant under quasi-isometry. Thus, it leads to a geometric property of finitely generated groups, also called the road trip property. The main result is that groups with the road trip property are finitely presented and satisfy a quadratic isoperimetric inequality. Examples of groups with the road trip property include hyperbolic, semihyperbolic, automatic and CAT(0) groups.
2008 ◽
Vol 18
(08)
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pp. 1243-1257
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2011 ◽
Vol 4
(6)
◽
pp. 341-343
2009 ◽
Vol 02
(02)
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pp. 171-182
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2011 ◽
Vol 61
(11)
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pp. 3218-3225
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Keyword(s):
1937 ◽
Vol 43
(10)
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pp. 717-720
Keyword(s):
2018 ◽
Vol 98
(3)
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pp. 422-433