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