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Surgery theory = foundations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Surgery theory/ by Wolfgang Lück, Tibor Macko.
其他題名:	foundations /
作者:	Lück, Wolfgang.
其他作者:	Macko, Tibor.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	xv, 956 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Manifolds and Cell Complexes. -
電子資源:	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:

1366170
Manifolds and Cell Complexes.

LC Class. No.: QA613.658

Dewey Class. No.: 514.72

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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.
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