University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > H_{4g-6}(M_g)

H_{4g-6}(M_g)

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact info@newton.ac.uk.

HHHW04 - Manifolds

The set of isomorphism classes of genus g Riemann surfaces carries a natural topology in which it may be locally parametrized by 3g-3 complex parameters. The resulting space is denoted M_g, the moduli space of Riemann surfaces, and is more precisely a complex orbifold of that dimension. The study of this space has a very long history involving many areas of mathematics, including algebraic geometry, group theory, and stable homotopy theory. The space M_g is not compact, essentially because a family of Riemann surface may degenerate into a non-smooth object, and may be compactified in several interesting ways. I will discuss a compactification due to Harvey, which looks like a compact real (6g-6)-dimensional manifold with corners, except for orbifold singularities. The combinatorics of the corner strata in this compactification may be encoded using graphs. Using this compactification, I will explain how to define a chain map from Kontsevich's graph complex to a chain complex calculating the rational homology of M_g. The construction is particularly interesting in degree 4g-6, where our methods give rise to many non-zero classes in H_{4g-6}(M_g), contradicting some predictions. This is joint work with Chan and Payne (arXiv:1805.10186).

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

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2020 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity