| 书目名称 | Real Homotopy of Configuration Spaces | | 副标题 | Peccot Lecture, Coll | | 编辑 | Najib Idrissi | | 视频video | http://file.papertrans.cn/823/822172/822172.mp4 | | 概述 | Provides an in-depth discussion of the connection between operads and configuration spaces.Describes a unified and accessible approach to the use of graph complexes.Based on 4 lectures held in the fra | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience. | | 出版日期 | Book 2022 | | 关键词 | Configuration Spaces of Manifolds; Operad Theory; Homotopy Invariants of Manifolds; Semi-algebraic Form | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-04428-1 | | isbn_softcover | 978-3-031-04427-4 | | isbn_ebook | 978-3-031-04428-1Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
| 1 |
Front Matter |
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Abstract
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| 2 |
,Overview of the Volume, |
Najib Idrissi |
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Abstract
In this chapter, we give a broad overview of the rest of this volume and we explain the key concepts. In the later chapters, we study these concepts in more detail. We give references to these more detailed explanations throughout this overview.
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| 3 |
,Configuration Spaces of Manifolds, |
Najib Idrissi |
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Abstract
In this chapter, we introduce configuration spaces of manifolds more precisely. We start by listing several of their applications and occurrences in mathematics in Sect. 2.1, including braid groups and surface braid groups, Goodwillie–Weiss calculus, Gelfand–Fuks cohomology, stable splitting of mapping spaces, iterated loop spaces, and stability.
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,Configuration Spaces of Closed Manifolds, |
Najib Idrissi |
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Abstract
In this chapter, we define the model conjectured by Lambrechts and Stanley (Algebr Geom Topol 8(2):1191–1222, 2008), and we show that their conjecture is true over . for a large class of closed manifolds.
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,Configuration Spaces of Manifolds with Boundary, |
Najib Idrissi |
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Abstract
The results of the previous chapter apply to closed manifolds, that is, compact manifolds without boundary. In this chapter, we extend these to manifolds with boundary. The case of manifolds with boundary is more difficult than the case of manifolds: in general, the homotopy types of the configuration spaces of a manifold with boundary . depend on the homotopy type of the pair (., .), not just the homotopy type of ..
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,Configuration Spaces and Operads, |
Najib Idrissi |
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Abstract
In this final chapter, we explain some of the connections that exist between configuration spaces and operads. Briefly, an operad is a device that encodes a category of algebras, such as associative algebras, commutative algebras, Lie algebras, and so on. In topology, they were introduced in the study of iterated loop spaces, which have a structure encoded by a certain class of operad, the little disks operads. These operads are central to the theory and appear in many applications.
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| 7 |
Back Matter |
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Abstract
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