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The Geometry Research Group at IME USP |
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| Mini-curso:
Pós Graduação do Programa do Mat-IME-USP.
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Course: |
Orbifolds, reflection groups, aspherical manifolds |
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Professor: |
Prof:Professor Michael Davis (Ohio State Universityniv, EUA) |
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Organized by: |
Prof. Claudio Gorodski. |
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Date and place: |
May: 12, 14, 16, 19 and 21 at 14h |
| Description: There is a classical theory of groups
generated by reflections on the classical spaces of constant
curvature: for each dimension n, we have the n-sphere,
Euclidean n-space and hyperbolic n-space. The underlying
group of such a reflection group is a "Coxeter group." This is a
fairly general notion, meaning only that the group is generated by
involutions and that it has a presentation of a certain
form. Although very few Coxeter groups arise from the classical
geometries, it turns out that any Coxeter group can be realized as a
reflection group acting properly and cocompactly on a certain
contractible cell complex. Gromov and Moussong showed that
this cell complex has a natural polyhedral metric of nonpositive
curvature so that the W-action is by isometries. The construction
of the cell complex and similar spaces has been used to provide
many interesting examples of aspherical manifolds. Papers on
these topics as well as slides from previous talks can be found at the
following link - >https://people.math.osu.edu/davis.12/
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