9 feb 2017 -- 17:30
Aula A1, Polo Fibonacci, Pisa
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.)