東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Lie models in topology

Buijs, Urtzi.

Linked to FindBook

Google Book

Amazon

博客來

Lie models in topology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lie models in topology/ by Urtzi Buijs ... [et al.].
other author:	Buijs, Urtzi.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xxv, 283 p. :ill., digital ;24 cm.
[NT 15003449]:	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
Subject:	Algebraic topology. -
Online resource:	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
LDR:02617nmm a2200337 a 4500 001 2257633
003 DE-He213
005 20210322105232.0
006 m d
007 cr nn 008maaau
008 220420s2020 sz s 0 eng d
020 $a 9783030544300 $q (electronic bk.)
020 $a 9783030544294 $q (paper)
024 7 $a 10.1007/978-3-030-54430-0 $2 doi
035 $a 978-3-030-54430-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612
072 7 $a PBPD $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBPD $2 thema
082 0 4 $a 514.2 $2 23
090 $a QA612 $b .L716 2020
245 0 0 $a Lie models in topology $h [electronic resource] / $c by Urtzi Buijs ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
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.
650 0 $a Algebraic topology. $3 532744
650 0 $a Lie algebras. $3 526115
650 1 4 $a Algebraic Topology. $3 891269
650 2 4 $a Category Theory, Homological Algebra. $3 899944
700 1 $a Buijs, Urtzi. $3 3529005
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Progress in mathematics ; $v v.335. $3 3529006
856 4 0 $u https://doi.org/10.1007/978-3-030-54430-0
950 $a Mathematics and Statistics (SpringerNature-11649)