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

Surgery theory = foundations /

Lück, Wolfgang.

Linked to FindBook

Google Book

Amazon

博客來

Surgery theory = foundations /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Surgery theory/ by Wolfgang Lück, Tibor Macko.
Reminder of title:	foundations /
Author:	Lück, Wolfgang.
other author:	Macko, Tibor.
Published:	Cham :Springer International Publishing : : 2024.,
Description:	xv, 956 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Introduction -- 2 The s-Cobordism Theorem -- 3 Whitehead Torsion -- 4 The Surgery Step and ξ-Bordism -- 5 Poincaré Duality -- 6 The Spivak Normal Structure -- 7 Normal Maps and the Surgery Problem -- 8 The Even-Dimensional Surgery Obstruction -- 9 The Odd-Dimensional Surgery Obstruction -- 10 Decorations and the Simple Surgery Obstruction -- 11 The Geometric Surgery Exact Sequence -- 12 Homotopy Spheres -- 13 The Geometric Surgery Obstruction Group and Surgery Obstruction -- 14 Chain Complexes -- 15 Algebraic Surgery -- 16 Brief Survey of Computations of L-Groups -- 17 The Homotopy Type of G/TOP, G/PL, and G/O -- 18 Computations of Topological Structure Sets of some Prominent Closed Manifolds -- 19 Topological Rigidity -- 20 Modified Surgery -- 21 Solutions of the Exercises.
Contained By:	Springer Nature eBook
Subject:	Surgery (Topology) -
Online resource:	https://doi.org/10.1007/978-3-031-56334-8
ISBN:	9783031563348

Surgery theory = foundations /
Lück, Wolfgang.

Surgery theoryfoundations /[electronic resource] :by Wolfgang Lück, Tibor Macko. - Cham :Springer International Publishing :2024. - xv, 956 p. :ill., digital ;24 cm. - Grundlehren der Mathematischen Wissenschaften, a series of comprehensive studies in mathematics,v. 3622196-9701 ;. - Grundlehren der Mathematischen Wissenschaften, a series of comprehensive studies in mathematics ;v. 362..

1 Introduction -- 2 The s-Cobordism Theorem -- 3 Whitehead Torsion -- 4 The Surgery Step and ξ-Bordism -- 5 Poincaré Duality -- 6 The Spivak Normal Structure -- 7 Normal Maps and the Surgery Problem -- 8 The Even-Dimensional Surgery Obstruction -- 9 The Odd-Dimensional Surgery Obstruction -- 10 Decorations and the Simple Surgery Obstruction -- 11 The Geometric Surgery Exact Sequence -- 12 Homotopy Spheres -- 13 The Geometric Surgery Obstruction Group and Surgery Obstruction -- 14 Chain Complexes -- 15 Algebraic Surgery -- 16 Brief Survey of Computations of L-Groups -- 17 The Homotopy Type of G/TOP, G/PL, and G/O -- 18 Computations of Topological Structure Sets of some Prominent Closed Manifolds -- 19 Topological Rigidity -- 20 Modified Surgery -- 21 Solutions of the Exercises.

This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.

ISBN: 9783031563348

Standard No.: 10.1007/978-3-031-56334-8doiSubjects--Topical Terms:

686611
Surgery (Topology)

LC Class. No.: QA613.658

Dewey Class. No.: 514.72

Surgery theory = foundations /
LDR:03198nmm a2200337 a 4500 001 2374409
003 DE-He213
005 20240706125234.0
006 m d
007 cr nn 008maaau
008 241231s2024 sz s 0 eng d
020 $a 9783031563348 $q (electronic bk.)
020 $a 9783031563331 $q (paper)
024 7 $a 10.1007/978-3-031-56334-8 $2 doi
035 $a 978-3-031-56334-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA613.658
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 514.72 $2 23
090 $a QA613.658 $b .L941 2024
100 1 $a Lück, Wolfgang. $3 3723256
245 1 0 $a Surgery theory $h [electronic resource] : $b foundations / $c by Wolfgang Lück, Tibor Macko.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2024.
300 $a xv, 956 p. : $b ill., digital ; $c 24 cm.
490 1 $a Grundlehren der Mathematischen Wissenschaften, a series of comprehensive studies in mathematics, $x 2196-9701 ; $v v. 362
505 0 $a 1 Introduction -- 2 The s-Cobordism Theorem -- 3 Whitehead Torsion -- 4 The Surgery Step and ξ-Bordism -- 5 Poincaré Duality -- 6 The Spivak Normal Structure -- 7 Normal Maps and the Surgery Problem -- 8 The Even-Dimensional Surgery Obstruction -- 9 The Odd-Dimensional Surgery Obstruction -- 10 Decorations and the Simple Surgery Obstruction -- 11 The Geometric Surgery Exact Sequence -- 12 Homotopy Spheres -- 13 The Geometric Surgery Obstruction Group and Surgery Obstruction -- 14 Chain Complexes -- 15 Algebraic Surgery -- 16 Brief Survey of Computations of L-Groups -- 17 The Homotopy Type of G/TOP, G/PL, and G/O -- 18 Computations of Topological Structure Sets of some Prominent Closed Manifolds -- 19 Topological Rigidity -- 20 Modified Surgery -- 21 Solutions of the Exercises.
520 $a This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
650 0 $a Surgery (Topology) $3 686611
650 1 4 $a Manifolds and Cell Complexes. $3 3538507
700 1 $a Macko, Tibor. $3 3723257
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Grundlehren der Mathematischen Wissenschaften, a series of comprehensive studies in mathematics ; $v v. 362. $3 3723258
856 4 0 $u https://doi.org/10.1007/978-3-031-56334-8
950 $a Mathematics and Statistics (SpringerNature-11649)