A homological characterization of hyperbolic groups |
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| Authors: | D J Allcock S M Gersten |
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| Institution: | (1) Mathematics Department, University of Utah, Salt Lake City, UT 84112, USA (E-mail address: allcock@math.utah.edu/gersten@math.utah.edu), US |
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| Abstract: | A finitely presented group G is hyperbolic iff H
(1)
1(G,ℝ)=0=(1)
2(G, ℝ), where H
(1)
* (resp. (1)
*) denotes the ℓ1-homology (resp. reduced ℓ1-homology). If Γ is a graph, then every ℓ1 1-cycle in Γ with real coefficients can be approximated by 1-cycles of compact support. A 1-relator group G is hyperbolic iff H
(1)
1(G,ℝ)=0.
Oblatum: 30-IV-1997 & 14-V-1998 / Published online: 14 January 1999 |
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| Keywords: | |
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