Configuration spaces and homological stability (or, what I did for the last three and a half years)
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Wed, 13/02 16:00 |
Martin Palmer (University of Oxford) |
Junior Geometric Group Theory Seminar  |
SR2 |
| First of all, I will give an overview of what the phenomenon of homological stability is and why it's useful, with plenty of examples. I will then introduce configuration spaces – of various different kinds – and give an overview of what is known about their homological stability properties. A "configuration" here can be more than just a finite collection of points in a background space: in particular, the points may be equipped with a certain non-local structure (an "orientation"), or one can consider unlinked embedded copies of a fixed manifold instead of just points. If by some miracle time permits, I may also say something about homological stability with local coefficients, in general and in particular for configuration spaces. | |||