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Local cohomology

Related publications (21)

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A note on topological amenability

Nicolas Monod

A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established. ...

Oxford University Press2010

On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

Nicolas Monod

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and gr ...

De Gruyter2010

Vanishing up to the rank in bounded cohomology

Nicolas Monod

We establish the vanishing for non-trivial unitary representations of the bounded cohomology of SLd up to degree d-1. It holds more generally for uniformly bounded representations on superreflexive spaces. The same results are obtained for lattices. We als ...

2007

An invitation to bounded cohomology

Nicolas Monod

A selection of aspects of the theory of bounded cohomology is presented. The emphasis is on questions motivating the use of that theory as well as on some concrete issues sugested by its study. Specific topics include rigidity, bounds on characteristic cla ...

European Mathematical Society2006

Orbit equivalence rigidity and bounded cohomology

Nicolas Monod

We establish new results and introduce new methods in the theory of measurable orbit equivalence. Our rigidity statements hold for a wide (uncountable) class of negatively curved groups. Amongst our applications are (a) measurable Mostow-type rigidity theo ...

2006

Stabilization for SLn in bounded cohomology

Nicolas Monod

We prove that for all local fields SLn is stable over n in terms of continuous bounded cohomology. We complement this by various computations in low degree, showing notably the vanishing of the third bounded cohomology of SLn(R) for all n. We link the corr ...

2004

Cocycle superrigidity and bounded cohomology for negatively curved spaces

Nicolas Monod

We introduce new techniques to extend superrigidity theory beyond the scope of Lie or algebraic groups. We construct a cohomological invariant which accounts for, and generalizes, all known superrigidity results for actions on negatively curved spaces. Tog ...

2004

Negative curvature from a cohomological viewpoint

Nicolas Monod

A note presenting a selection of results that are elaborated upon in Cocycle superrigidity and bounded cohomology for negatively curved spaces and Orbit equivalence rigidity and bounded cohomology. Proofs are given for illustrative "toy-cases". ...

2003

On and around the bounded cohomology of SL2

Nicolas Monod

We establish how the spectral decomposition for a Riemann surface determines the allocation of the bounded cohomology over the representations of SL2(R). Then we explore the connections of the Dilogarithm with the continuous bounded cohomology of SL2(R) an ...

Springer2002

Continuous bounded cohomology and applications to rigidity theory

Nicolas Monod

The central theme of this paper is a product formula for (continuous) bounded cohomology, and more specifically its applications to rigidity theory for lattices — both in Lie/algebraic groups and more general topological groups. A more condensed exposition ...

2002