GTA Seminar | Speaker: Mark Grant (University of Aberdeen)

Title: Immersed but not embedded homology classes 

Abstract:  An integral homology class z in a smooth manifold N is “Steenrod representable” if z=f_*[M] for some closed smooth oriented manifold M and continuous map f: M - > N. Further, z is “immersed”, resp. “embedded”, if f can be chose to be an immersion, resp. embedding. Thom showed that not every class is Steenrod representable, and examples are known of classes which are Steenrod representable but not embedded. In this talk, I will describe examples which are: (a) immersed but not embedded, and (b) Steenrod representable but not immersed.
This is joint work with Diarmuid Crowley, prompted by a MathOverflow question by Zhenhua Liu.