語系:
繁體中文
English
說明(常見問題)
圖資館首頁
登入
回首頁
到查詢結果
[ subject:"Algebraic Topology." ]
切換:
標籤
|
MARC模式
|
ISBD
Lie models in topology
~
Buijs, Urtzi.
Lie models in topology
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Lie models in topologyby 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.
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$q(electronic bk.)
Lie models in topology
Lie models in topology
[electronic resource] /by Urtzi Buijs ... [et al.]. - Cham :Springer International Publishing :2020. - xxv, 283 p. :ill., digital ;24 cm. - Progress in mathematics,v.3350743-1643 ;. - Progress in mathematics ;v.295..
Background -- The Quillen functors L and C, and their duals -- Complete differential graded Lie algebras -- Maurer-Cartan elements and the Deligne groupoid -- The Lawrence-Sullivan Interval -- The cosimplicial cdgl L -- The model and realization functors -- A model category for cdgl -- The cosimplicial cdgl L via transfer -- The Deligne-Getzler-Hinich functor MC and equivalence of realizations -- Examples -- Index of notation.
Since the birth of rational homotopy theory, the possibility of extending the Quillen approach - in terms of Lie algebras - to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
ISBN: 9783030544300$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
LDR
:02617nmm a2200337 a 4500
001
591538
003
DE-He213
005
20210322105232.0
006
m d
007
cr nn 008maaau
008
210629s2020 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
189702
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
856
4 0
$u
https://doi.org/10.1007/978-3-030-54430-0
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
全部
電子館藏
館藏
1 筆 • 頁數 1 •
1
條碼號
館藏地
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
000000192547
電子館藏
1圖書
電子書
EB QA612 .L716 2020 2020
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
多媒體檔案
https://doi.org/10.1007/978-3-030-54430-0
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼
登入