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Rational Homotopy Theory Ii [Kietas viršelis]

(Univ Of Maryland, Usa), (Univ D'angers, France), (Univ Catholique De Louvain, Belgium)
  • Formatas: Hardback, 448 pages
  • Išleidimo metai: 27-Apr-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814651427
  • ISBN-13: 9789814651424
Kitos knygos pagal šią temą:
Rational Homotopy Theory IiDidesnis paveikslėlis
  • Formatas: Hardback, 448 pages
  • Išleidimo metai: 27-Apr-2015
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814651427
  • ISBN-13: 9789814651424
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789814651424.html
Raktažodžiai:
This research monograph is a detailed account with complete proofs of rational homotopy theory for general non-simply connected spaces, based on the minimal models introduced by Sullivan in his original seminal article. Much of the content consists of new results, including generalizations of known results in the simply connected case. The monograph also includes an expanded version of recently published results about the growth and structure of the rational homotopy groups of finite dimensional CW complexes, and concludes with a number of open questions.This monograph is a sequel to the book Rational Homotopy Theory [ RHT], published by Springer in 2001, but is self-contained except only that some results from [ RHT] are simply quoted without proof.
Preface x
Introduction xi
1 Basic definitions and constructions 1(44)
1.1 Graded algebra
1(5)
1.2 Differential graded algebra
6(2)
1.3 Simplicial sets
8(6)
1.4 Polynomial differential forms
14(4)
1.5 Sullivan algebras
18(6)
1.6 The simplicial and spatial realizations of a ^-algebra
24(6)
1.7 Homotopy and based homotopy
30(5)
1.8 The homotopy groups of a minimal Sullivan algebra
35(10)
2 Homotopy Lie algebras and Sullivan Lie algebras 45(46)
2.1 The homotopy Lie algebra of a minimal Sullivan algebra
45(3)
2.2 The fundamental Lie algebra of a Sullivan 1-algebra
48(6)
2.3 Sullivan Lie algebras
54(2)
2.4 Primitive Lie algebras and exponential groups
56(7)
2.5 The lower central series of a group
63(8)
2.6 The linear isomorphism (^ sV)# congruent to UL
71(4)
2.7 The fundamental group of a 1-finite minimal Sullivan algebra
75(6)
2.8 The homology Hopf algebra of a 1-finite minimal Sullivan algebra
81(3)
2.9 The action of GL on πn(|^V,d|,*)
84(3)
2.10 Formal Sullivan 1-algebras
87(4)
3 Fibrations and ^-extensions 91(26)
3.1 Fibrations, Serre fibrations and homotopy fibrations
91(2)
3.2 The classifying space fibration and Postnikov decompositions of a connected CW complex
93(2)
3.3 A-extensions
95(6)
3.4 Existence of minimal Sullivan models
101(6)
3.5 Uniqueness of minimal Sullivan models
107(4)
3.6 The acyclic closure of a minimal Sullivan algebra
111(3)
3.7 Sullivan extensions and fibrations
114(3)
4 Holonomy 117(28)
4.1 Holonomy of a fibration
117(8)
4.2 Holonomy of a ^-extension
125(5)
4.3 Holonomy representations for a ^-extension
130(3)
4.4 Nilpotent and locally nilpotent representations
133(4)
4.5 Connecting topological and Sullivan holonomy
137(5)
4.6 The holonomy action on the homotopy groups of a fibre
142(3)
5 The model of the fibre is the fibre of the model 145(24)
5.1 The main theorem
145(15)
5.2 The holonomy action of π1(Y,*) on π*(F)
160(4)
5.3 The Sullivan model of a universal covering space
164(2)
5.4 The Sullivan model of a spatial realization
166(3)
6 Loop spaces and loop space actions 169(26)
6.1 The loop cohomology coalgebra of (^V, d)
169(7)
6.2 The transformation map ηL
176(7)
6.3 The graded Hopf algebra, H*(|^U|:Q)
183(4)
6.4 Connecting Sullivan algebras with topological spaces
187(8)
7 Sullivan spaces 195(32)
7.1 Sullivan spaces
195(4)
7.2 The classifying space BG
199(6)
7.3 The Sullivan 1-model of BG
205(8)
7.4 Malcev completions
213(5)
7.5 The morphism m|^v,d|:(^V,d)->APL(|^V,d|)
218(4)
7.6 When BG is a Sullivan space
222(5)
8 Examples 227(18)
8.1 Nilpotent and rationally nilpotent groups
227(1)
8.2 Nilpotent and rationally nilpotent spaces
227(2)
8.3 The groups Z#...#Z
229(2)
8.4 Semidirect products
231(1)
8.5 Orientable Riemann surfaces
232(5)
8.6 The classifying space of the pure braid group Pn is a Sullivan space
237(1)
8.7 The Heisenberg group
238(1)
8.8 Seifert manifolds
239(1)
8.9 Arrangement of hyperplanes
240(1)
8.10 Connected sum of real projective spaces
241(1)
8.11 A final example
242(3)
9 Lusternik-Schnirelmann category 245(22)
9.1 The LS category of topological spaces and commutative cochain algebras
245(3)
9.2 The mapping theorem
248(1)
9.3 Module category and the Toomer invariant
249(1)
9.4 cat = mcat
250(10)
9.5 cat = e(-)#
260(1)
9.6 Jessup's Theorem
261(4)
9.7 Example
265(2)
10 Depth of a Sullivan algebra and of a Sullivan Lie algebra 267(34)
10.1 Ext, Tor and the Hochschild-Serre spectral sequence
267(5)
10.2 The depth of a minimal Sullivan algebra
272(4)
10.3 The depth of a Sullivan Lie algebra
276(3)
10.4 Sub Lie algebras and ideals of a Sullivan Lie algebra
279(8)
10.5 Depth and relative depth
287(8)
10.6 The radical of a Sullivan Lie algebra
295(3)
10.7 Sullivan Lie algebras of finite type
298(3)
11 Depth of a connected graded Lie algebra of finite type 301(12)
11.1 Summary of previous results
301(3)
11.2 Modules over an abelian Lie algebra
304(3)
11.3 Weak depth
307(6)
12 Trichotomy 313(16)
12.1 Overview of results
313(4)
12.2 The rationally elliptic case
317(1)
12.3 The rationally hyperbolic case
317(1)
12.4 The gap theorem
318(1)
12.5 Rationally infinite spaces of finite category
319(6)
12.6 Rationally infinite CW complexes of finite dimension
325(4)
13 Exponential growth 329(38)
13.1 The invariant log index
331(2)
13.2 Growth of graded Lie algebras
333(4)
13.3 Weak exponential growth and critical degree
337(6)
13.4 Approximation of log index L
343(7)
13.5 Moderate exponential growth
350(8)
13.6 Exponential growth
358(9)
14 Structure of a graded Lie algebra of finite depth 367(22)
14.1 Introduction
367(1)
14.2 The spectrum
368(4)
14.3 Minimal sub Lie algebras
372(5)
14.4 The weak complements of an ideal
377(3)
14.5 L-equivalence
380(7)
14.6 The odd part of a graded Lie algebra
387(2)
15 Weight decompositions of a Sullivan Lie algebra 389(12)
15.1 Weight decompositions
389(4)
15.2 Exponential growth of L
393(2)
15.3 The fundamental Lie algebra of 1-formal Sullivan algebra
395(6)
16 Problems 401(4)
Bibliography 405(4)
Index 409