论文标题
拓扑e_n-operads的Koszul二元性
Koszul duality for topological E_n-operads
论文作者
论文摘要
我们表明，光谱中e_n-operad的koszul双重偶性是o（n）等效等同于其n折的悬浮。为此，我们引入了一个新的O（n） - 欧（eclidean spaces r_n），barycentric Operad，它是纤维上的单纯形，并具有同构形态为结构地图。我们还介绍了其限制的小n盘D_N的子上映，这是E_N-OPERAD。 The duality is realized by an unstable explicit S-duality pairing (F_n)_+ \smash BD_n \to S_n, where B is the bar-cooperad construction, F_n is the Fulton-MacPherson E_n-operad, and the dualizing object S_n is an operad of spheres that are one-point compactifications of star-shaped neighbourhoods in R_n.我们还将Operad包含映射e_n \ e_ {n+m}的Koszul双重识别为（N+M） - 不稳定的Operad Map e_ {n+m} \ toσ^m e_n的（N+M） - 折叠desuspension。
We show that the Koszul dual of an E_n-operad in spectra is O(n)-equivariantly equivalent to its n-fold desuspension. To this purpose we introduce a new O(n)-operad of Euclidean spaces R_n, the barycentric operad, that is fibred over simplexes and has homeomorphisms as structure maps; we also introduce its sub-operad of restricted little n-discs D_n, that is an E_n-operad. The duality is realized by an unstable explicit S-duality pairing (F_n)_+ \smash BD_n \to S_n, where B is the bar-cooperad construction, F_n is the Fulton-MacPherson E_n-operad, and the dualizing object S_n is an operad of spheres that are one-point compactifications of star-shaped neighbourhoods in R_n. We also identify the Koszul dual of the operad inclusion map E_n \to E_{n+m} as the (n+m)-fold desuspension of an unstable operad map E_{n+m} \to Σ^m E_n defined by May.
