Framed discs operads and Batalin-Vilkovisky algebras
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Framed discs operads and Batalin-Vilkovisky algebras. / Salvatore, Paolo; Wahl, Nathalie.
In: Quarterly Journal of Mathematics, Vol. 54, 2003, p. 213-231.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 54
SP - 213
EP - 231
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
ER -
ID: 9396708