Manchester Geometry Seminar 2001/2002

[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 S^n₀ by attaching maps non-trivially. For an arbitrary spectrum Y with bottom cell S^n₀ and π_n0Y cyclic, a core is a map X->Y inducing a monomorphism in homotopy and an isomorphism on π_n0.

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 is always nuclear and that CP^∞₍₂₎, HP^∞₍₂₎, ko₍₂₎ and ku₍₂₎ are nuclear.