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Nicolas Monod

Related publications (62)

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The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012

A lattice in more than two Kac–Moody groups is arithmetic

Nicolas Monod

Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma i ...

2012

A fixed point theorem for L1 spaces

Nicolas Monod

We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...

Springer-Verlag2012

Is an irng singly generated as an ideal?

Nicolas Monod

Recall that a rng is a ring which is possibly non-unital. In this note, we address the problem whether every finitely generated idempotent rng (abbreviated as irng) is singly generated as an ideal. It is well-known that it is the case for a commutative irn ...

World Scientific Publishing2012

Decomposing locally compact groups into simple pieces

Nicolas Monod

We present a contribution to the structure theory of locally compact groups. The emphasis is put on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact sub ...

Cambridge University Press2011

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

The Dixmier problem, lamplighters and Burnside groups

Nicolas Monod

J.Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Fur ...

2010

Product groups acting on manifolds

Nicolas Monod

We analyse volume-preserving actions of product groups on Riemannian manifolds. Under a natural spectral irreducibility assumption, we prove the following dichotomy: Either the action is measurably isometric, in which case there are at most two factors; or ...

2009

Isometry groups of non-positively curved spaces: Structure Theory

Nicolas Monod

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat- ...

2009

The norm of the Euler class

Nicolas Monod

We prove that the norm of the Euler class

\mathcal{E}

for flat vector bundles is

2^{-n}

(in even dimension

n

, since it vanishes in odd dimension). This shows that the Sullivan-Smillie bound considered by Gromov and Ivanov-Turaev is sharp. We construc ...

Springer Verlag2012