Framed disc operads and the equivariant recognition principle
نویسندگان
چکیده
The framed n-discs operad fDn 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 fDn is equivalent to the n-fold loop space on a SO(n)-space. Examples of fD2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fDn. Koszul duality for semidirect product operads of chain complexes is defined and applied to compute the double loop space homology as BV-algebra. MSC(2000): 55P48, 18D10.
منابع مشابه
Framed Discs Operads and Batalin–vilkovisky Algebras
The framed n-discs operad f Dn 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 f Dn is equivalent to the n-fold loop space on an SO(n)-space. Examples of f D2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of f Dn , which produces higher Batalin–Vilko...
متن کاملOperadic Multiplications in Equivariant Spectra, Norms, and Transfers
We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N∞ operads, equivariant generalizations of E∞ operads. Algebras in equivariant spectra over an N∞ operad model homotopically commutative equivariant ring spectra that only admit certain collections of Hill-Hopkins-Ravenel norms, determined by the operad. Analogously, algebras in equivar...
متن کاملResearch Plan
My current main project concerns the study of the interaction between the theory of operads and genuine equivariant homotopy theory. Briefly, an operad (introduced by May in [13]) consists of a sequence On of sets/spaces of “n-ary operations” together with Σn-actions and suitable compositions. The main point of operad theory is then the study of the algebras over a fixed operad O, which are o...
متن کاملMonoidal Bousfield Localizations and Algebras over Operads
We give conditions on a monoidal model category M and on a set of maps C so that the Bousfield localization of M with respect to C preserves the structure of algebras over various operads. This problem was motivated by an example due to Mike Hill which demonstrates that for the model category of equivariant spectra, preservation does not come for free, even for cofibrant operads. We discuss thi...
متن کاملBousfield Localization and Algebras over Operads
We give conditions on a monoidal model category M and on a set of maps S so that the Bousfield localization of M with respect to S preserves the structure of algebras over various operads. This problem was motivated by an example due to Mike Hill which demonstrates that for the model category of equivariant spectra, even very nice localizations can fail to preserve commutativity. As a special c...
متن کامل