Online talk

 https://princeton.zoom.us/j/92750870921?pwd=UVhrenRlcXZxYXRhZFk3NnJaVFltdz09

Producing explicit type n finite spectra, such as Smith-Toda complexes or generalized Moore spectra, is a difficult problem that is closely related to periodicity in the stable homotopy groups of spheres. Finite spectra are in some sense dual to fp spectra in the sense of Mahowald-Rezk, like ko or tmf. Using genuine equivariant homotopy, we produce a new family of fp spectra at the prime 2 and each chromatic height, known as (connective) higher real K-theories. Using an Euler characteristic for fp spectra defined by Ishan Levy, we use these theories to put constraints on the existence of small finite spectra. This results in a lower bound for the number of obstructions to producing a Smith-Toda complex and new constraints on the exponents of the vi that can appear in a generalized Moore spectrum, valid at all heights. This is joint work with Mike Hill.