Tobias Ekholm 氏 (University of Uppsala)

Abstract:

Immersions of spheres into Euclidean spaces are classified up to
regular homotopy by their Smale invariants. We shall discuss
geometric formulas for Smale invariants primarily in dimensions
right below double.

The set of self-transverse immersions is open and dense in the
space of immersions. The regular homotopy classification of
immersiosn is concerned with finding the path components of the
space of immersions. We will consider the finer classification
problem of finding the path components of the space of
self-tansverse immersions. An important tool in this study are so
called Vassiliev invariants. We show that in some dimensions
Vassiliev invariants are too weak to distinguish the path
components of the space of self-transverse immersions. In other
cases the theory of Vassiliev invariants is much richer. We will
describe what is known in these cases and state some open
problems.