Topology Seminar

Hurewicz Images of Real Johnson-Wilson Theories and a recomputation of $ER(2)^*RP^\infty$

Guchuan Li, Northwestern

Wednesday, November 1st, 2017
3:40 PM - 4:40 PM
Hylan 1106A

We show that the Hopf elements, the Kervaire classes, and the $\bar{\kappa}$ family in the stable homotopy groups of spheres are detected by the $C_2$-fixed points of the Real Brown-Peterson spectrum under the Hurewicz map. A subset of these families is detected by the $C_2$-fixed points of the Real Johnson-Wilson theories, depending on the height. As an application, we use the knowledge of the Hurewicz images and attaching maps in $RP^\infty$ to give a recomputation of $ER(2)_*RP^\infty$, which is computed by Kitchloo and Wilson in their work of non immersions of $RP^n$. This is a joint work with Xiaolin Danny Shi, Guozhen Wang and Zhouli Xu.

Event contact: carl dot mctague at rochester dot edu