Context-free manifold calculus and the Fulton-MacPherson Operad
Context-free manifold calculus and the Fulton-MacPherson Operad
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上下文无关流形微积分和 Fulton-MacPherson Operad
DOI：
10.2140/agt.2013.13.1243
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
V. Tourtchine
中科院分区：
文献类型：
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作者：
V. Tourtchine
本文利用框架Fulton-MacPherson算子上截断模的映射空间给出了Weiss嵌入塔的一个显式描述。组织的文件在第1节中，我们概述了一个一般框架的上下文自由流形演算和它的连接到框架盘操作。这种方法的细节由P. Boavida de Brito和M.韦斯在[4]中。他们工作的主要结果之一是定理1.5，它描述了韦斯泰勒塔的上下文自由拓扑预层在流形上的截断右模映射的框架盘operad。第1节是为了强调这样一个事实，即对于这种描述，人们可以使用框架圆盘的操作数，其通常的和离散的拓扑结构。定理1.5的一个离散形式出现在G. Arone和作者[2]。第二部分是主要的结构。在定理2.1中，我们用框架Fulton-MacPherson操作数代替框架圆盘操作数，并描述Weiss对一个流形嵌入到另一个流形的空间Emb（M，N）的逼近Tk Emb（M，N），用后一个操作数上的截断右模的映射表示。所讨论的右模本身自然地从流形M和N中框架位形空间的Axelrod-Singer-Fulton-MacPherson紧化得到。这种嵌入塔的描述类似于古德威利-克莱因-韦斯构造[12]和辛哈的一维结点空间模型[18，19]。定理2.1的证明非常简单，不依赖于Boavida-Weiss定理1.5。第3和第4部分做这个工作。此外，我们的构造可以用来给出定理1.5的另一种证明，如第5节所示。第6节给出了我们的构造的另一个应用，描述了关于Fulton-MacPherson算子上截断无穷小双模映射的长嵌入空间的韦斯塔。作为推论，我们得到：当n > m+2时，空间Embc（R，R）等价于Bm上的无穷小双模范畴中小圆盘Bm和Bn的操作数之间的导映射空间. 2010年数学学科分类。主要：57 Q45;次要：18 D50、55 P48、55 P99。
The paper gives an explicit description of theWeiss embedding tower in terms of spaces of maps of truncated modules over the framed Fulton-MacPherson operad. Organization of the paper In Section 1 we outline a general framework of context free manifold calculus and its connection to the framed discs operad. The details of this approach were completed by P. Boavida de Brito and M. Weiss in [4]. One of the main results of their work is Theorem 1.5 that describes the Weiss Taylor tower of a context free topological presheaf on a manifold in terms of maps of truncated right modules over the framed discs operad. Section 1 is given to emphasize the fact that for this description one can use the operad of framed discs with both its usual and discrete topology. A discrete version of Theorem 1.5 appeared earlier in a work of G. Arone and the author [2]. Section 2 is where the main construction is given. In Theorem 2.1 we replace the framed discs operad by the framed Fulton-MacPherson operad and describeWeiss’ approximations Tk Emb(M,N) to the space Emb(M,N) of embeddings of one manifold into another in terms of maps of truncated right modules over the latter operad. The right modules in question themselves are naturally obtained from the Axelrod-Singer-Fulton-MacPherson compactifications of framed configuration spaces in manifolds M and N . This description of the embedding tower resembles both the Goodwillie-Klein-Weiss construction [12] and also Sinha’s models [18, 19] for spaces of one dimensional knots. The proof of Theorem 2.1 is very straighforward and does not rely on the Boavida-Weiss Theorem 1.5. Sections 3 and 4 do this job. Moreover our construction can be used to give an alternative proof of Theorem 1.5 which is shown in Section 5. Section 6 produces another application of our construction describing Weiss’ tower for spaces of long embeddings in terms of maps of truncated infinitesimal bimodules over the Fulton-MacPherson operad. As a corollary we obtain that for n > m+2 the space Embc(R ,R) is equivalent to the space of derived maps between the operads of little discs Bm and Bn in the category of infinitesimal bimodules over Bm. 2010 Mathematics Subject Classification. Primary: 57Q45; Secondary: 18D50, 55P48, 55P99.
流形微积分和同伦滑轮
DOI：
10.4310/hha.2013.v15.n2.a20
发表时间：
2013
期刊：
Homology, Homotopy and Applications
影响因子：
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作者：
Boavida De Brito P
通讯作者：
Boavida De Brito P