Jules Chenal (University of Lille) - On the Topology of Real Equivariant Torus Embeddings

In this talk, I will present a joint work with Matilde Manzaroli. I will introduce real tori (in the greater generality) as well as real equivariant torus embeddings. Then I will describe the structure of the torus orbits. It will allow us to easily compute the Betti numbers of the real loci of smooth real equivariant torus embeddings, provided that those real loci are compact. Then I will present a canonical "foliation" of their real loci by equivariant embeddings of split tori. I will express a necessary and sufficient condition for this foliation to be given by the fibre of a fibre bundle, and explain how to reduce to this case by performing toric blow-ups.