The framed n-discs operad fD(n) is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by fD(n) is equivalent to the n-fold loop space on an SO(n)-space. Examples of fD(2)-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fD(n), which produces higher Batalin-Vilkovisky algebra structures for n even. We study quadratic duality for semidirect product operads and compute the double loop space homology of a manifold as BV-algebra.

Salvatore, P., & Wahl, N. (2003). Framed discs operads and Batalin-Vilkovisky algebras. QUARTERLY JOURNAL OF MATHEMATICS, 54(2), 213-231 [10.1093/qmath/hag012].

Framed discs operads and Batalin-Vilkovisky algebras

SALVATORE, PAOLO;
2003

Abstract

The framed n-discs operad fD(n) is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by fD(n) is equivalent to the n-fold loop space on an SO(n)-space. Examples of fD(2)-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fD(n), which produces higher Batalin-Vilkovisky algebra structures for n even. We study quadratic duality for semidirect product operads and compute the double loop space homology of a manifold as BV-algebra.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
English
Salvatore, P., & Wahl, N. (2003). Framed discs operads and Batalin-Vilkovisky algebras. QUARTERLY JOURNAL OF MATHEMATICS, 54(2), 213-231 [10.1093/qmath/hag012].
Salvatore, P; Wahl, N
Articolo su rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/45249
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