Andrew Baker (University of Glasgow)
[This is joint work with Peter May following on from a paper by Ho-Kriz-May]
A p-local cellular spectrum X is called nuclear of dimension n0 if it is obtained from the sphere Sn0 by attaching maps non-trivially. For an arbitrary spectrum Y with bottom cell Sn0 and πn0Y cyclic, a core is a map X->Y inducing a monomorphism in homotopy and an isomorphism on πn0.
As a motivating example, Priddy proved a long time ago that BP was nuclear. It follows easily that BP->MU is a core.
I will discuss some properties of cores and some techniques for identifying
them. In particular, it follows that BP