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Person# Nicolas Monod

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Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined f

Hyperbolic group

In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group equipped with a word met

Simple group

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely

Courses taught by this person (3)

MATH-100(a): Advanced analysis I

Nous étudions les concepts fondamentaux de l'analyse, le calcul différentiel et intégral de fonctions réelles d'une variable.

MATH-315: Spaces of non-positive curvature and groups

Non-positive curvature is a fundamental aspect of geometry appearing in Euclidean spaces, hyperbolic spaces, trees, buildings and many more spaces. We study it with the general but powerful tool of CA

MATH-416: Analysis on groups

We study analytic phenomena on groups, notably paradoxical decompositions and fixed point properties.

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Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate the relevance of nilpotent groups for Ulam's problem.

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range of coefficients. This implies the same vanishing for a number of groups with self-similarity properties, such as Thompson's group F. In particular, these groups are boundedly acyclic. Our method is ergodic and applies to "large" transformation groups where the Mather-Matsumoto-Morita method sometimes fails because not all are acyclic in the usual sense.

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring generated by the bounded Euler class. These seem to be the first examples of groups for which the entire bounded cohomology can be described without being trivial. We further prove that the C-r-diffeomorphisms groups of the circle and of the closed 2-disc have the same bounded cohomology as their homeomorphism groups, so that both differ from the ordinary cohomology of C-r-diffeomorphisms when r > 1. Finally, we determine the low-dimensional bounded cohomology of homeo-and dif-feomorphism of the spheres S-n and of certain 3-manifolds. In particular, we answer a question of Ghys by showing that the Euler class in H-4(Homeo(?)(S-3)) is unbounded.