We are interested in properties of the comparison map between bounded continuous cohomology and (unbounded)

continuous cohomology of a topological group G, in particular whetherit is an isomorphism.

While in discrete case the question has been mostly settled, even for semisimple Lie groups very little is known.

The concept of bornology formalizes idea of boundedness, similar to how topology does it for continuity. It is

used extensively in functional analysis to study bounded linear operators.

We propose a notion of bornological manifolds that may provide a framework that allows us to put geometric group

properties, topological dynamics and analytic properties of topological vector spaces together, and use sheaf-theoretic

methods to address this question.

This is join work with Kobi Kremnitzer.

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