# Knots, Galois groups and Massey products – Claudio Quadrelli (Università di Firenze)

#### Abstract

Cohomological Massey products were defined in the ’50s as higher cohomology operations generalizing the cup product, to provide a “cohomological translation” of the Milnor invariants, which describe the higher linking properties of the knots in a link. After introducing Massey products, I will tell how they have been employed recently to understand the structure of Galois groups of fields: in particular, there are deep analogies between the Galois groups of certain extensions of $\mathbb{Q}$ and the fundamental groups of links (e.g., there is an arithmetic analogue of the Borromean rings!), whereas groups with “non-vanishing” Massey products do not occur as absolute Galois groups of fields. (No advanced knowledge in algebra — nor in algebraic topology — is required.) Il seminario si terrà nell’Aula A1 del Polo Fibonacci.

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