Framed discs operads and Batalin-Vilkovisky algebras

TY - JOUR

T1 - Framed discs operads and Batalin-Vilkovisky algebras

AU - Salvatore, Paolo

AU - Wahl, Nathalie

N1 - Keywords: math.AT; math.QA; 55P48; 18D10

PY - 2003

Y1 - 2003

N2 - 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 a SO(n)-space. Examples of fD_2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fD_n. Koszul duality for semidirect product operads of chain complexes is defined and applied to compute the double loop space homology as BV-algebra.

AB - 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 a SO(n)-space. Examples of fD_2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fD_n. Koszul duality for semidirect product operads of chain complexes is defined and applied to compute the double loop space homology as BV-algebra.

M3 - Journal article

SN - 0033-5606

VL - 54

SP - 213

EP - 231

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

ER -