A central question of algebraic topology is to understand homotopy classes of maps between finite cell complexes. The Nilpotence Theorem of Hopkins-Devinatz-Smith together with the Periodicity Theorem of Hopkins-Smith describes non-nilpotent self maps of finite spectra. The Morava K- theories \(K(n)_*\) are extraordinary cohomology theories which detect whether a finite spectrum X supports a \(v_n\) self map. Such maps are known to exist for each finite spectrum $X$ for an appropriate \(n\) but few explicit examples are known. Working at the prime 2, we use a technique of Palmieri- Sadofsky to produce algebraic analogs of \(v_n\) maps that are easier to detect and compute. We reproduce the existence proof of Adams’s \(v_1^4\) map on the Mod 2 Moore spectrum, and work towards a \(v_2^i\) map for a small value of \(i\).

Pretalk 3-3:45 pm in Hylan 1106B.