Batalin-Vilkovisky algebras and the J-homomorphism
Abstract
Description
Let X be a topological space. The homology of the iterated loop space $H_*Ω^n X$ is an algebra over the homology of the framed n-disks operad $H_*f\mathcal{D}_n$ \cite{Getzler:BVAlg,Salvatore-Wahl:FrameddoBVa}. We determine completely this $H_*f\mathcal{D}_n$-algebra structure on
$H_*(Ω^n X;\mathbb{Q})$. We show that the action of $H_*(SO(n))$ on the iterated loop space $H_*Ω^n X$ is related to the J-homomorphism and that the BV-operator vanishes on spherical classes only in characteristic other than 2.
12 pages
12 pages