Applications of cellular E_2-algebras

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• Oscar Randal-Williams, Cambridge
• Wednesday 16 November 2016, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Many families of moduli spaces, such as moduli spaces of Riemann surfaces or graphs, can be given the structure of an E_2-algebra: that is, a multiplication law which is as commutative as that of a 2-fold loop space. In the case of Riemann surfaces it is given by boundary connect-sum. I will explain a new technique which allows up to construct these as “cellular E_2-algebras” with strong constraints on the dimensions of the cells which appear. The phenomenon of homological stability is an immediate consequence of such cell structures, but this point of view leads to further “secondary” stability phenomena also.

This is joint with S. Galatius and A. Kupers.

This talk is part of the Differential Geometry and Topology Seminar series.

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