Batalin-Vilkovisky algebras and the J-homomorphism |
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| Authors: | Gerald Gaudens |
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| Institution: | a Mathematisches Institut, Beringstrasse 1, D-53115 Bonn, Germany
b UMR 6093 associée au CNRS, Université d'Angers, Faculté des Sciences, 2 Boulevard Lavoisier, 49045 Angers, France |
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| Abstract: | Let X be a topological space. The homology of the iterated loop space H∗ΩnX is an algebra over the homology of the framed n-disks operad H∗fDn 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∗fDn-algebra structure on H∗(ΩnX;Q). We show that the action of H∗(SO(n)) on the iterated loop space H∗ΩnX is related to the J-homomorphism and that the BV-operator on H∗(Ω2X) vanishes on spherical classes only in characteristic other than 2. |
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| Keywords: | 55P35 55P62 55Q50 |
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