**
Michael
Albanese,
Department
of
Pure
Mathematics,
University
of
Waterloo**

**
"Spin^h
and
further
generalisations
of
spin"**

The question of which manifolds are spin or spin^c has a simple and complete answer. In this talk we address the same question for the lesser known spin^h manifolds which have appeared in geometry and physics in recent decades. We determine the first obstruction to being spin^h and use this to provide an example of an orientable manifold which is not spin^h. The existence of such an example leads us to consider an infinite sequence of generalised spin structures. In doing so, we determine an answer to the following question: is there an integer k such that every manifold embeds in a spin manifold with codimension at most k?

This is joint work with Aleksandar Milivojevic.

MC 5417