國立虎尾科技大學 |

Lie Models in Topology

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Lie Models in Topology/ by Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré.
作者:	Buijs, Urtzi.
其他作者:	Tanré, Daniel.
面頁冊數:	XXV, 283 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
電子資源:	https://doi.org/10.1007/978-3-030-54430-0
ISBN:	9783030544300

Lie Models in Topology
Buijs, Urtzi.

Lie Models in Topology[electronic resource] /by Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré. - 1st ed. 2020. - XXV, 283 p.online resource. - Progress in Mathematics,3350743-1643 ;. - Progress in Mathematics,312.

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:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA612-612.8

Dewey Class. No.: 514.2

Lie Models in Topology
LDR:03021nam a22004095i 4500 001 1030847
003 DE-He213
005 20201215090529.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030544300 $9 978-3-030-54430-0
024 7 $a 10.1007/978-3-030-54430-0 $2 doi
035 $a 978-3-030-54430-0
050 4 $a QA612-612.8
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
100 1 $a Buijs, Urtzi. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327848
245 1 0 $a Lie Models in Topology $h [electronic resource] / $c by Urtzi Buijs, Yves Félix, Aniceto Murillo, Daniel Tanré.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XXV, 283 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Progress in Mathematics, $x 0743-1643 ; $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 2 4 $a Category Theory, Homological Algebra. $3 678397
650 1 4 $a Algebraic Topology. $3 672209
650 0 $a Homological algebra. $3 1255326
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Algebraic topology. $3 678206
700 1 $a Tanré, Daniel. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327851
700 1 $a Murillo, Aniceto. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327850
700 1 $a Félix, Yves. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327849
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030544294
776 0 8 $i Printed edition: $z 9783030544317
776 0 8 $i Printed edition: $z 9783030544324
830 0 $a Progress in Mathematics, $x 0743-1643 ; $v 312 $3 1258196
856 4 0 $u https://doi.org/10.1007/978-3-030-54430-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)