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＜電子ブック＞
Lie Models in Topology / by Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré
(Progress in Mathematics. ISSN:2296505X ; 335)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2020
大きさ	XXV, 283 p : online resource
著者標目	*Buijs, Urtzi author Félix, Yves author Murillo, Aniceto author Tanré, Daniel author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Algebra, Homological FREE:Algebraic Topology FREE:Category Theory, Homological Algebra
一般注記	Background -- The Quillen functors L and C , and their duals -- Complete differential graded Lie algebras -- Maurer-Cartan elements and the Deligne groupoid -- The Lawrence-Sullivan Interval -- The cosimplicial cdgl L -- The model and realization functors -- A model category for cdgl -- The cosimplicial cdgl L via transfer -- The Deligne-Getzler-Hinich functor MC and equivalence of realizations -- Examples -- Index of notation Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics HTTP:URL=https://doi.org/10.1007/978-3-030-54430-0

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