Batalin-Vilkovisky algebras and the J-homomorphism

2007/07/20 by Gerald Gaudens, Gaudens, Gerald, Luc Menichi +1
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #History and Overview (math.HO) #math.AT #math.GR #math.GT #math.HO

paper · pdf · doi:10.48550/arxiv.0707.3103

12 pages

arxiv created 2007/07/20 · arxiv updated 2009/12/01

Abstract

Let X be a topological space. The homology of the iterated loop space H_*Ωⁿ X is an algebra over the homology of the framed n-disks operad H_*fD_n \citeGetzler:BVAlg,Salvatore-Wahl:FrameddoBVa. We determine completely this H_*fD_n-algebra structure on H_*(Ωⁿ X;ℚ). We show that the action of H_*(SO(n)) on the iterated loop space H_*Ωⁿ X is related to the J-homomorphism and that the BV-operator vanishes on spherical classes only in characteristic other than 2.

Related

• Relations in the modulo 2 homology of framed disks algebras
• A Batalin-Vilkovisky algebra morphism from double loop spaces to free loops
• The bv algebra in string topology of classifying spaces
• String topology and the based loop space
• Homotopy Batalin-Vilkovisky algebras