Gästforskare föreläste om $H=G\circ F$ och harmoniska morfismer

Besöket genomfördes via ett STINT-projekt som drivs av Aurélio Menegon och Andreas Lind. Under besöket hölls bland annat seminarier av Raimundo Araújo Dos Santos och Maico Ribeiro.

Seminarie med Raimundo Araújo Dos Santos

Fibrations on the compositions of singularities: Milnor fibers and boundaries

Abstract: We will show how to relate the Milnor fibers of the composition of a singular map germ $H=G\circ F$ by using the component map germs F and G. For that, we will characterize the called “tameness” condition of H as a function of singular map germs F and G, and also the Milnor tubes of F, G and H. Using that, we will relate the Milnor fibers of F, G and H and its Milnor boundaries. It time permits, we will show some Euler characteristic relating all these topological data.

Seminarie med Maico Ribeiro

Harmonic morphisms and their Milnor fibrations

Abstract: In this work, we advance in the understanding of the relationships between germs of harmonic morphisms and Milnor fibrations. In this sense, we show that every harmonic morphism between Euclidean spaces defines a Milnor fibration in the tube and sphere and these fibrations are equivalent. Moreover, we present new examples of harmonic morphisms and generalize the main result of P. Baird and Ye-Lin Ou, which ensures,with a special hypothesis over a germ of a harmonic morphism, that the Milnor sphere fibration is itself a harmonic morphism.

This is a join work with R. N. Araújo dos Santos (ICMC-USP), D. Dreibelbis (UNF) and G. Murphy (UNF).