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Oscar Randal–Williams: The Torelli Lie algebra

Time: Tue 2022-01-25 14.15 - 16.00

Location: Zoom

Video link: Meeting ID: 921 756 1880

Participating: Oscar Randal–Williams (University of Cambridge)

Abstract: The Mal'cev Lie algebra associated to the Torelli group of a surface was completely determined by Hain (1993), who gave an explicit presentation which is quadratic if the genus is at least 4. I will explain some work, joint with A. Kupers, which exploits the formal similarity between surfaces and certain higher-dimensional manifolds to prove some new results about this Lie algebra: it is stably Koszul, and the geometric Johnson homomorphism is (nearly) stably injective.