Elliptic Artin Monoids and Higher Homotopy Groups

Data Seminario: 
Ora Inizio: 
Ora Fine: 
Kyoji Saito
Kavli IPMU, Japan

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.

Il seminario si terrà in Aula Magna del Dipartimento.

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