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Lie models in topology

Buijs, Urtzi.

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Lie models in topology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lie models in topology/ by Urtzi Buijs ... [et al.].
其他作者:	Buijs, Urtzi.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xxv, 283 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Algebraic topology. -
電子資源:	https://doi.org/10.1007/978-3-030-54430-0
ISBN:	9783030544300

Lie models in topology
Lie models in topology[electronic resource] /by Urtzi Buijs ... [et al.]. - Cham :Springer International Publishing :2020. - xxv, 283 p. :ill., digital ;24 cm. - Progress in mathematics,v.3350743-1643 ;. - Progress in mathematics ;v.335..

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.

ISBN: 9783030544300

Standard No.: 10.1007/978-3-030-54430-0doiSubjects--Topical Terms:

532744
Algebraic topology.

LC Class. No.: QA612

Dewey Class. No.: 514.2

Lie models in topology
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505 0 $a 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.
520 $a 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.
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