论文标题
偏置空间
The Disc-structure space
论文作者
论文摘要
我们研究了一个紧凑的平滑歧管$ m $的脱节空间$ s^{\ rm disc} _ \ partial（m）$。从非正式的角度来看，该空间衡量$ m $，以及其差异性的差异，以及$ m $的有序框架配置空间图，以及它们之间的点删除和点拆分图，以及其派生的自动形态。作为主要结果，我们表明，在高维度中，偏置空间a）仅取决于$ m $，b）的切向2型的无限环空间，而c）只要$ m $是旋转的。证据涉及可能具有独立关注的中间结果，包括加强嵌入微积分与界限类别的水平，取决于合理化的派生的绘制映射空间的行为，以及对Dwyer和Hess问题的答案，我们证明了地图$ {\ rm btop}（\ rm btop} $ is _;当且仅当$ d $最多为$ 2 $时，等价。
We study the Disc-structure space $S^{\rm Disc}_\partial(M)$ of a compact smooth manifold $M$. Informally speaking, this space measures the difference between $M$, together with its diffeomorphisms, and the diagram of ordered framed configuration spaces of $M$ with point-forgetting and point-splitting maps between them, together with its derived automorphisms. As the main results, we show that in high dimensions, the Disc-structure space a) only depends on the tangential 2-type of $M$, b) is an infinite loop space, and c) is nontrivial as long as $M$ is spin. The proofs involve intermediate results that may be of independent interest, including an enhancement of embedding calculus to the level of bordism categories, results on the behaviour of derived mapping spaces between operads under rationalisation, and an answer to a question of Dwyer and Hess in that we show that the map ${\rm BTop}(d)\to {\rm BAut}(E_d)$ is an equivalence if and only if $d$ is at most $2$.
