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Lie models in topology

Buijs, Urtzi.

Lie models in topology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lie models in topologyby Urtzi Buijs ... [et al.].
other author:	Buijs, Urtzi.
Published:	Cham :Springer International Publishing :2020.
Description:	xxv, 283 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Algebraic topology.
Online resource:	https://doi.org/10.1007/978-3-030-54430-0
ISBN:	9783030544300$q(electronic bk.)

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.295..

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$q(electronic bk.)

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

189702
Algebraic topology.

LC Class. No.: QA612

Dewey Class. No.: 514.2

Lie models in topology
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245 0 0 $a Lie models in topology $h [electronic resource] / $c by Urtzi Buijs ... [et al.].
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300 $a xxv, 283 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.335
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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650 0 $a Lie algebras. $3 191078
650 1 4 $a Algebraic Topology. $3 273784
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Buijs, Urtzi. $3 883098
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Progress in mathematics ; $v v.295. $3 558269
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