Title: Multidegree and Sp(1)-principal bundles over the seven-sphere
Speaker: Solenn Estier - University of Geneva
Abstract: The determination of the possible degrees of maps between closed oriented manifolds of same dimension is a well-studied question. In this talk, we focus on a refinement called the multidegree of a map, in the specific case of sphere bundles over spheres. Following work by Lafont and Neofytidis, Wang and Kennedy, we restrict to principal S^3-bundles over spheres, and will present a work in progress, aiming to apply homotopical methods to provide necessary and sufficient conditions to the existence of maps with given multidegree. We use the fact that many spaces under scrutiny admit an H-space structure, along with a simple CW-structure, to extend maps using the so-called Puppe sequence of a cofibration.