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5. Lp-cohomology

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Lp-cohomology is a quantitative version of cohomology of topological spaces, well suited for a geometric study of noncompact spaces and groups. It has been used with partial success in connection with problems in high-dimensional topology (Singer's conjecture on the Euler characteristic of aspherical manifolds), low-dimensional topology (Cannon's conjecture on groups whose boundary is a 2-sphere), Riemannian geometry (optimal curvature pinching) and coarse geometry (hyperbolic locally compact groups, coarse embeddings between nilpotent or hyperbolic groups). The course will provide background on these problems and be as self-contained as possible.

Duration: 9 lectures.

1. What Lp-cohomology has been good for
2. L\infty cohomology and (Kähler) hyperbolic groups
3. Lp dimension and the ideal boundary of hyperbolic groups
4. Quasi-isometry invariance
5. Large scale conformal invariance
6. Classification of hyperbolic locally compact groups
7. Curvature pinching

This talk is part of the Isaac Newton Institute Seminar Series series.

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