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Article Dans Une Revue Topology and its Applications Année : 2008

Batalin–Vilkovisky algebras and the J-homomorphism

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Résumé

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 D n [E. Getzler, Batalin–Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (2) (1994) 265–285; P. Salvatore, N. Wahl, Framed discs operads and Batalin–Vilkovisky algebras, Q. J. Math. 54 (2) (2003) 213–231]. We explicitly determine this H f D n -algebra structure on H ( Ω n X ; 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 on H ( Ω 2 X ) vanishes on spherical classes only in characteristic other than 2.

Dates et versions

hal-03040211 , version 1 (04-12-2020)

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Gerald Gaudens, Luc Menichi. Batalin–Vilkovisky algebras and the J-homomorphism. Topology and its Applications, 2008, 156 (2), pp.365 - 374. ⟨10.1016/j.topol.2008.07.013⟩. ⟨hal-03040211⟩
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