Low-dimensional topology and algebraic geometry

Low-dimensional topology and algebraic geometry Math Department of the Higher School of Economics, Room 413 Thursday, November 16, 12:00-13:30

Website: https://math.hse.ru/lowdimtop/

Speaker: Roman Krytovsky

Title: Dehn's lemma and the loop theorem (Part 2)

Abstract:

I will prove Dehn's lemma, which roughly says that if you have an embedding of the boundary of a 2-disk into the boundary of a 3-manifold, then you can extend the mapping to an embedding of the
whole disk into this 3-manifold. A central part of the proof will be a tower construction due to Papakyriakopoulos.
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Speaker: Balaram Usov

Title: The mapping class groups of surfaces (Part 2)

Abstract:

In this talk I will define the mapping class group of a surface. We will compute this group for the torus and prove an important theorem that this group is finitely generated by Dehn twists. In doing so I will define a complex of curves and mention some of its properties.