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Rational Homotopy Theory and Differential Forms 2nd ed. 2013 [Kietas viršelis]

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  • Formatas: Hardback, 227 pages, aukštis x plotis: 235x155 mm, weight: 4853 g, 46 Illustrations, black and white; XI, 227 p. 46 illus., 1 Hardback
  • Serija: Progress in Mathematics 16
  • Išleidimo metai: 02-Oct-2013
  • Leidėjas: Birkhauser Boston Inc
  • ISBN-10: 1461484677
  • ISBN-13: 9781461484677
Kitos knygos pagal šią temą:
Rational Homotopy Theory and Differential Forms 2nd ed. 2013Didesnis paveikslėlis
  • Formatas: Hardback, 227 pages, aukštis x plotis: 235x155 mm, weight: 4853 g, 46 Illustrations, black and white; XI, 227 p. 46 illus., 1 Hardback
  • Serija: Progress in Mathematics 16
  • Išleidimo metai: 02-Oct-2013
  • Leidėjas: Birkhauser Boston Inc
  • ISBN-10: 1461484677
  • ISBN-13: 9781461484677
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781461484677.html
Raktažodžiai:
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Thams theorem on simplicial complexes. In addition, Sullivans results on computing the rational homotopy type from forms is presented.  





New to the Second Edition:

*Fully-revised appendices including an expanded discussion of the Hirsch lemma

*Presentation of a natural proof of a Serre spectral sequence result

*Updated content throughout the book, reflecting advances in the area of homotopy theory





With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Recenzijos

From the book reviews:

This book is a second, augmented version of one of the famous books on rational homotopy. The topological intuition throughout the book, the recollections of the necessary elementary homotopy theory and the list of exercises make this book an excellent introduction to Sullivans theory. this book is highly recommended to anyone who wants to understand Sullivans theory of rational homotopy theory. (Daniel Tanré, Mathematical Reviews, February, 2015)

1 Introduction 1(4)
2 Basic Concepts 5(16)
2.1 CW Complexes
5(3)
2.2 First Notions from Homotopy Theory
8(5)
2.3 Homology
13(6)
2.4 Categories and Functors
19(2)
3 CW Homology Theorem 21(6)
3.1 The Statement
21(1)
3.2 The Proof
22(2)
3.3 Examples
24(3)
4 The Whitehead Theorem and the Hurewicz Theorem 27(14)
4.1 Definitions and Elementary Properties of Homotopy Groups
27(2)
4.2 The Whitehead Theorem
29(2)
4.3 Completion of the Computation of πn(Sn)
31(2)
4.4 The Hurewicz Theorem
33(1)
4.5 Corollaries of the Hurewicz Theorem
34(4)
4.6 Homotopy Theory of a Fibration
38(1)
4.7 Applications of the Exact Homotopy Sequence
39(2)
5 Spectral Sequence of a Fibration 41(12)
5.1 Introduction
41(1)
5.2 Fibrations- over a Cell
42(1)
5.3 Generalities on Spectral Sequences
43(2)
5.4 The Leray-Serre Spectral Sequence of a Fibration
45(3)
5.5 Examples
48(5)
6 Obstruction Theory 53(10)
6.1 Introduction
53(1)
6.2 Definition and Properties of the Obstruction Cocycle
54(3)
6.3 Further Properties
57(1)
6.4 Obstruction to the Existence of a Section of a Fibration
58(1)
6.5 Examples
58(5)
7 Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations 63(6)
7.1 Relation of Cohomology and Eilenberg-MacLane Spaces
63(1)
7.2 Principal K(π, n)-Fibrations
64(5)
8 Postnikov Towers and Rational Homotopy Theory 69(14)
8.1 Rational Homotopy Theory for Simply Connected Spaces
73(6)
8.2 Construction of the Localization of a Space
79(4)
9 deRham's Theorem for Simplicial Complexes 83(12)
9.1 Piecewise Linear Forms
83(2)
9.2 Lemmas About Piecewise Linear Forms
85(3)
9.3 Naturality Under Subdivision
88(1)
9.4 Multiplicativity of the deRham Isomorphism
89(1)
9.5 Connection with the Cinfinity deRham Theorem
90(2)
9.6 Generalizations of the Construction
92(3)
10 Differential Graded Algebras 95(8)
10.1 Introduction
95(2)
10.2 Hirsch Extensions
97(2)
10.3 Relative Cohomology
99(1)
10.4 Construction of the Minimal Model
100(3)
11 Homotopy Theory of DGAs 103(10)
11.1 Homotopies
103(1)
11.2 Obstruction Theory
104(3)
11.3 Applications of Obstruction Theory
107(2)
11.4 Uniqueness of the Minimal Model
109(4)
12 DGAs and Rational Homotopy Theory 113(6)
12.1 Transgression in the Serre Spectral Sequence and the Duality
113(1)
12.2 Hirsch Extensions and Principal Fibrations
114(1)
12.3 Minimal Models and Postnikov Towers
115(2)
12.4 The Minimal Model of the deRham Complex
117(2)
13 The Fundamental Group 119(8)
13.1 1-Minimal Models
119(1)
13.2 π1 Q
120(3)
13.3 Functorality
123(2)
13.4 Examples
125(2)
14 Examples and Computations 127(14)
14.1 Spheres and Projective Spaces
127(1)
14.2 Graded Lie Algebras
128(1)
14.3 The Borromean Rings
129(2)
14.4 Symmetric Spaces and Formality
131(1)
14.5 The Third Homotopy Group of a Simply Connected Space
132(2)
14.6 Homotopy Theory of Certain 4-Dimensional Complexes
134(1)
14.7 Q-Homotopy Type of BUn and Un
135(2)
14.8 Products
137(1)
14.9 Massey Products
138(3)
15 Functorality 141(10)
15.1 The Functorial Correspondence
141(3)
15.2 Bijectivity of Homotopy Classes of Maps
144(4)
15.3 Equivalence of Categories
148(3)
16 The Hirsch Lemma 151(14)
16.1 The Cubical Complex and Cubical Forms
151(3)
16.2 Hirsch Extensions and Spectral Sequences
154(2)
16.3 Polynomial Forms for a Serre Fibration
156(3)
16.4 Serre Spectral Sequence for Polynomial Forms
159(4)
16.5 Proof of Theorem 12.1
163(2)
17 Quillen's Work on Rational Homotopy Theory 165(12)
17.1 Differential Graded Lie Algebras
165(1)
17.2 Differential Graded Co-algebras
166(1)
17.3 The Bar Construction
167(2)
17.4 Relationship Between Quillen's Construction and Sullivan's
169(1)
17.5 Quillen's Construction
169(8)
18 Ainfinity-Structures and Cinfinity-Structures 177(10)
18.1 Operads, Rooted Trees, and Stasheff's Associahedron
177(4)
18.2 Ainfinity-Algebras and Ainfinity-Categories
181(2)
18.3 Cinfinity-Algebras and DGAs
183(4)
19 Exercises 187(36)
References 223