Abstract
In his celebrated 1982 I.H.É.S. paper Volume and bounded cohomology [69], M. Gromov considers the singular bounded cohomology H• b(M) of a manifold M and proves a spray of deep and surprising theorems on the geometry of manifolds. This cohomology H• b(M) is defined exactly like usual singular cohomology, except that all cochains are required to be bounded. Similarly, one can define for a group Г the bounded cohomology H• b(Г) by the usual inhomogeneous complex with the only change that one restricts attention to bounded cochains : \( O \to R \to \ell ^\infty \left( {\Gamma ,R} \right) \to \ell ^\infty \left( {\Gamma ^2 ,R} \right) \to \bullet \bullet \bullet \)
Keywords
- Compact Group
- Spectral Sequence
- Mapping Class Group
- Countable Group
- Topological Isomorphism
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). Introduction. In: Monod, N. (eds) Continuous Bounded Cohomology of Locally Compact Groups. Lecture Notes in Mathematics, vol 1758. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44962-0_1
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DOI: https://doi.org/10.1007/3-540-44962-0_1
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Print ISBN: 978-3-540-42054-5
Online ISBN: 978-3-540-44962-1
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