Tamarkin, D.E.: Formality of chain operad of little discs. The framed little 2-discs operad is homotopy equivalent to a cyclic operad. If an operad C acts on X and Y is homotopy equivalent to X, then W C acts on Y. Sullivan, D.: Infinitesimal computations in topology. Santos, F.G., Navarro, V., Pascual, P., Roig, A.: Moduli spaces and formal operads. the homology of the framed little discs operad. In: Elliptic Cohomology, volume 342 of London Math. Cohen and Jones instead give a homotopy-theoretic description of the loop product in terms of a ring. Morava, J.: The motivic Thom isomorphism. Notes from a seminar at Stockholm University organized by Torsten Ekedahl and Sergei Merkulov. Merkulov, S.: Grothendieck-Teichmüller group in algebra, geometry and quantization: a survey. of GT(Q) Q×, proven by Drinfel’d, that D2 is a formal operad. Lambrechts, P., Volic, I.: Formality of the little \(N\)-disks operad. Kontsevich, M.: Operads and motives in deformation quantization. Kim, M.: Weights in cohomology groups arising from hyperplane arrangements. ![]() In: The Grothendieck Theory of Dessins d’Enfants (Luminy, 1993), volume 200 of London Math. 29(3), 245–274 (1975)ĭrinfel’d, V.: On quasitriangular quasi-Hopf algebras and on a group that is closely connected with \(\). This expository paper aims to be a gentle introduction to the topology of configuration spaces, or equivalently spaces of little disks. Congress, Montreal, Que., (1975)ĭeligne, P., Griffiths, P., Morgan, J., Sullivan, D.: Real homotopy theory of Kähler manifolds. the framed little discs operad, which is known to govern BV-algebras. Abstract This expository paper aims to be a gentle introduction to the topology of configuration spaces, or equivalently spaces of little disks. In: Proceedings of the International Congress of Mathematicians (Vancouver, BC, 1974), vol. using algebraic invariants such as homology and cohomology. 52, 137–252 (1980)ĭeligne, P.: Poids dans la cohomologie des variétés algébriques. Abstract:The framed little 2-discs operad is homotopy equivalent to a cyclic operad. I'm sure that I am misleading something.Bar-Natan, D.: On associators and the Grothendieck-Teichmuller group. $\gamma$ is not a topological morfism between $D_1\times D_2\rightarrow \gamma(D_1, D_2)$ then how I can create a element from $f$ and $g$ in the homotopy group of $\gamma(D_1,D_2)$. H(C2,k) of the little square operad C2, for which double. ![]() But I have a problem when I try to understand this like an Operad morfism because if we have two element $f$ in the homotopy group of a disc with one hole $D_1$ and $g$ in disc with two holes $D_2$ and $\gamma$ the operator in the structure of little disc operad, what is $\gamma(f,g)$ in the homotopy group of the disc with two holes $\gamma(D_1,D_2)$?. More precisely, as shown in Cohen 3, Br is isomorphic to the homology operad. ![]() Then I can forget about which type of operad really is and take the homotopy group of each element in a configuration space. 1 The space of n-ary operations of the little discs operad is a K (pi,1) for pi the braid group. I thought this is a Set operad and not a Top operad but I'm not sure.Ģ) If We have a topological spaces I know we can create the homotopy group. I'm starting to research in this area and I have some questions.ġ) I don't understand why little discs operad is a topological space, what is the topology of the configuration space of n discs? I know each element of the configuration space is a topological space (like a disc with holes) but the morfisms that is used there goes between the configutarions spaces, not between the discs. Cohen C1, C2 the algebras over the homology of the little discs operad. I want to understand what means the homotopy of the little discs operad. The equivalence of spineless cacti and the little discs operad is one of the.
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