Seminar Algebra and Geometry: Pascal Rolli (ETH Zürich)

Quasimorphisms and defect spaces

A quasimorphism (QM) is a real-valued function on a group that almost behaves like a homomorphism. Non-trivial QMs exist whenever the group has some features of negative curvature, for example when it is Gromov hyperbolic. I will discuss old and new constructions of QMs, using combinatorial, geometric and algebraic ideas. In a second part I will talk about the relation to cohomology. To each QM there is an associated class in the group's second bounded cohomology $H^2_b$. One of our QM constructions yields linear isometric embeddings so called defect spaces into $H^2_b$. These spaces have an interesting geometry, they are l^∞ spaces equipped with an exotic norm.

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