Ricordo a tutti che Bernard Perron e' da oggi ospite del dipartimento per alcune settimane, e terra' un corso (nell'ambito della scuola di dottorato); riporto qui di seguito l'abstract.

Bernard Perron

Fox differential Calculus revisited. Applications to mapping class group of surfaces and low dimension topology.

Abstract: We begin by a review of Fox differential Calculus. Using this Calculus we associate to any homeomorphism of surface a Fox matrix whose entries belong to the group ring of the fundamental group of the surface. From this we obtain a fair generalization of Johnson homomorphisms, defined on various subgroups of the mapping class group. This allows us to recover very easily deep results of Morita on the mapping class group.

Using the first part, we compute the Casson invariant of a 3-homology sphere obtained by gluing two handlebodies along a homeomorphism of the boundary belonging to the Torelli subgroup.

The third part (if we have time), still using Fox Calculus, will be on the definition of a homotopy intersection theory on surfaces and punctured 2-disk, with applications to mapping class group and braid group.

La prima lezione (durante la quale si fissera' anche il calendario successivo) avra' luogo domani 4/5/04 nell'aula 1.

Riccardo Benedetti