EVENT DETAILS AND ABSTRACT

Title: Algebraic v_n self maps at the prime 2
Speaker: Leanne Merrill
Speaker Info: University of Oregon
Brief Description:
Special Note:
Abstract:

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 vn-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 vn maps that are easier to detect and compute. We reproduce the existence proof of Adams's v14 map on the Mod 2 Moore spectrum, and work towards a v2i map for a small value of i.