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Vi scrivo per annunciarvi che questo giovedì vi sarà un seminario in presenza per il ciclo di seminari "Seminario di Combinatoria, Teoria di Lie e Topologia” di Pisa. Il seminario si svolgerà in Aula Magna dalle 15 alle 17 (con una breve pausa in mezzo). L'oratore è Kyoji Saito (Kavli IPMU, Tokyo).

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Titolo: Elliptic Artin Monoids and Higher Homotopy Groups

​Abstract: A half century ago when simply elliptic singularity was introduced, it was a natural question whether its discriminant complement is a K(π, 1) space. At that time, Fulvio Lazzeri suggested a possibility of existence of a non-trivial π2 class by a heuristic argument on the real discriminant complement.

In the present talk, I approach this problem from elliptic Artin monoids, where the monoid is defined by generalizing the classical Artin braid relations to the new relations, called elliptic braid relations, defined on elliptic diagrams. Contraly to the classical Artin monoids, the elliptic Artin monoids are not cancellative and their natural homomorphisms to elliptic Artin groups (=the fundamental groups of the elliptic discriminant complements) are not injective (except for rank 1 case). This fact leads to me to a construction of π2-classes in the complement of the discriminant. We conjecture that they are non-vanishing.

Then, we reformulate the classical K(π, 1)-conjecture for complements of discriminants, whether the discriminant complements are homotopic to classifying spaces associated to the elliptic Artin monoids.

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Francesco