Pure Math Grad Student Seminar (PuMaGraSS)

Speaker: Andy Senger

Title: (Non-)immersions of real projective spaces

Abstract: Given a smooth manifold M, it is a classical problem in differential topology to find the smallest n such that M immerses in R^n. In fact, the celebrated Hirsch-Smale theorem reduces this problem to a purely homotopical one. In this talk, I will explore some of the ways in which methods from homotopy theory can be used to prove (non-)immersion results, focusing on the concrete case of real projective spaces.