Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces

Sakasai, Takuya

Winter Braids VI (Lille, 2016), Winter Braids Lecture Notes (2016), Exposé no. 4, 25 p.

This article is the notes of a series of lectures in the workshop “Winter Braids VI”, Lille, in February 2016. We begin by recalling fundamental facts on mapping class groups of surfaces and overview the theory of Johnson homomorphisms developed by Johnson himself and Morita. Then we see how this theory is extended as invariants of homology cobordisms of surfaces and discuss an application to knot theory.

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