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The Second Bounded Cohomology of a Group Acting on a Gromov‐Hyperbolic Space
Author(s) -
Fujiwara K
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000033
Subject(s) - mathematics , cohomology , bounded function , hyperbolic group , riemannian manifold , hyperbolic space , pure mathematics , group (periodic table) , group action , group cohomology , relatively hyperbolic group , manifold (fluid mechanics) , space (punctuation) , knot (papermaking) , combinatorics , mathematical analysis , hyperbolic manifold , hyperbolic function , physics , quantum mechanics , chemical engineering , engineering , mechanical engineering , linguistics , philosophy
Suppose a group G acts on a Gromov‐hyperbolic space X properly discontinuously. If the limit set L ( G ) of the action has at least three points, then the second bounded cohomology group of G , H b 2 ( G ; R ) is infinite dimensional. For example, if M is a complete, pinched negatively curved Riemannian manifold with finite volume, then H b 2 ( π 1 ( M ) ; R ) is infinite dimensional. As an application, we show that if G is a knot group with G≄Z , then H b 2 ( G ; R ) is infinite dimensional. 1991 Mathematics Subject Classification : primary 20F32; secondary 53C20, 57M25.