Rational homotopy theory:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Series: | Graduate texts in mathematics
205 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 521 - 530 |
| Physical Description: | XXXII, 535 S. graph. Darst. : 24 cm |
| ISBN: | 0387950680 |
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MARC
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| 245 | 1 | 0 | |a Rational homotopy theory |c Yves Félix ; Stephen Halperin ; Jean-Claude Thomas |
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| 490 | 1 | |a Graduate texts in mathematics |v 205 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction
Table of Examples
I Homotopy Theory, Resolutions for Fibrations, and P-
local Spaces
0
1
(a) CW complexes
(b) Homotopy groups
(c) Weak homotopy type
(d) Cofibrations and
(e) Adjunction spaces
(f) Cones, suspensions, joins and smashes
2
(a) Fibrations
(b) Topological monoids and G-fibrations
(c) The homotopy fibre and the holonomy action
(d) Fibre bundles and principal bundles
(e) Associated bundles, classifying spaces, the
the holonomy fibration
3
(a) Graded modules and complexes
(b) Graded algebras
(c) Differential graded algebras
(d) Graded
(e)
4
(a) Basic definitions, (normalized) singular chains
(b) Topological products, tensor products and the dgc, C*(X k).
(c) Pairs, excision, homotopy and the Hurewicz homomorphism
(d) Weak homotopy equivalences
(e) Cellular homology and the Hurewicz theorem
(f) Eilenberg-MacLane spaces
5
xx CONTENTS
6
(a) Semifree models
(b) Quasi-isomorphism theorems
7
8
(a) The chain algebra of a topological monoid
(b) Semifree chain models
(c) The quasi-isomorphism theorem
(d) The Whitehead-Serre theorem
9
(a) P-local spaces
(b) Localization
(c) Rational homotopy type
II Sullivan Models
10
(a) Simplicial sets and simplicial cochain algebras
(b) The construction of A(K)
(c) The simplicial commutative cochain algebra
(d) The simplicial cochain algebra Cpl
(e) Integration and the
11
(a) Smooth manifolds
(b) Smooth differential forms
(c) Smooth singular simplices
(b) (d) The weak equivalence ADR(M) ~ APL(M;R)
12
(a) Sullivan algebras and models: constructions and examples
(b) Homotopy in Sullivan algebras
(c) Quasi-isomorphisms, Sullivan representatives, uniqueness of mini¬
mal models and formal spaces
(d) Computational examples
(e) Differential forms and geometric examples
13
(a) Morphisms and quasi-isomorphisms
(b) Adjunction spaces
(c) Homotopy groups
(d) Cell attachments
Rational
(e)
14
(a) The semifree property, existence of models and homotopy
(b) Minimal Sullivan models
15
(a) Models of fibrations
(b) Loops on spheres. Eilenberg-MacLane spaces and spherical fibrations200
(c) Pullbacks and maps of fibrations
(d) Homotopy groups
(e) The long exact homotopy sequence
(f) Principal bundles, homogeneous spaces and Lie group actions
16
(a) The loop space homology algebra
(b) The minimal Sullivan model of the path space fibration
(c) The rational product decomposition of
(d) The primitive subspace of
(e)
к)
17
(a) The Milnor realization of a simplicial set
(b) Products and fibre bundles
(c) The Sullivan realization of a commutative cochain algebra
(d) The spatial realization of a Sullivan algebra
(e) Morphisms and continuous maps
(f) Integration, chain complexes and products
III Graded Differential Algebra (continued)
18
(a) Bigraded modules and spectral sequences
(b) Filtered differential modules
(c) Convergence
(d) Tensor products and extra structure
19
20
(a) Projective
(b) Graded Ext and Tor
(c)
(d) Semifree resolutions
xxi¡
IV Lie Models
21
(a) Universal enveloping algebras
(b) Graded
(c) Free graded Lie algebras
(d) The homotopy Lie algebra of a topological space
(e) The homotopy Lie algebra of a minimal Sullivan algebra
(f
22
(a) Graded
(b)
(c) The properties of
(d)
(e)
(f) Free Lie models
23
(a) The constructions C*(L,di), and £(A,d)
(b) The homotopy Lie algebra and the Milnor-Moore spectral sequence
(c) Cohomology with coefficients
24
(a) Free Lie models of topological spaces
(b) Homotopy and homology in a Lie model
c) Suspensions and wedges of spheres
(d) Lie models for adjunction spaces
(e) CW complexes and chain Lie algebras
(f) Examples
(g) Lie model for a homotopy fibre
25
(a) The topological group,
(b)
(c)
(d) Morphisms of chain Lie algebras and the holonomy action
26
(a) Dga homotopy
(b) The
(c) The chain algebra quasi-isomorphism
(d) The proof of Theorem
Rational
V Rational Lusternik Schnirelmann Category
27
(a) LS category of spaces and maps
(b) Ganea s fibre-cofibre construction
(c) Ganea spaces and LS category
(d) Cone-length and LS category: Ganea s theorem
(e) Cone-length and LS category: Cornea s theorem
(f) Cup-length, c(A ; k) and Toomer s invariant, e{X;lz)
28
(a) Rational LS category
(b) Rational cone-length
(c) The mapping theorem
(d) Gottlieb groups
29
(a) The rational cone-length of spaces and the product length of models
(b) The LS category of a Sullivan algebra
(c) The mapping theorem for Sullivan algebras
(d) Gottlieb elements
(e) Hess theorem
(f) The model of (AV,d)
(g) The Milnor-Moore spectral sequence and Ginsburg s theorem
(h) The invariants meat and
30
(a) Rational LS category of products
(b) Rational LS category of fibrations
(c) The mapping theorem for a fibre inclusion
31
(a) The holonomy representation for a Sullivan model
(b) Local nilpotence and local conilpotence
(c)
(d) Proof of Jessup s theorem
(e) Examples
(f) Iterated Lie brackets
VI The Rational Dichotomy:
Elliptic and Hyperbolic Spaces
and
Other Applications
32
xxiv CONTENTS
(a) Pure Sullivan algebras
(b) Characterization of elliptic Sullivan algebras
(c) Exponents and formal dimension
(d)
(e) Rationally elliptic topological spaces
(f) Decomposability of the loop spaces of rationally elliptic spaces
33
(a) Exponential growth of rational homotopy groups
(b) Spaces whose rational homology is finite dimensional
(c) Loop space homology
34
(a) Horn. Ext, tensor and Tor for t/X-modules
(b) The Hochschild-Serre spectral sequence
(c) Coefficients in UL
35
(a) Complexes of finite length
(b) Qy-spaces and C»
(c) The Milnor resolution of
(d)
(e) The depth of
(f)
(g)
36
(a) Depth and grade
(b) Solvable Lie algebras and the radical
(c) Noetherian enveloping algebras
(d) Locally nilpotent elements
(e) Examples
37
(a) The homology of the homotopy fibre,
(b)
(c) Inert element
(d) The homotopy Lie algebra of a spherical 2-cone
(e) Presentations of graded Lie algebras
(f
38
(b) Properties of
(b) Elliptic spaces
(c) LS
(d) Inert elements
Rational Homotopy
39
References
Index 531
|
| any_adam_object | 1 |
| author | Félix, Yves 1951- Halperin, Stephen 1942- Thomas, Jean-Claude |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| ctrlnum | (OCoLC)247403970 (DE-599)BVBBV013646219 |
| dewey-full | 514.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.24 |
| dewey-search | 514.24 |
| dewey-sort | 3514.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T18:49:31Z |
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| isbn | 0387950680 |
| language | English French |
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| spelling | Félix, Yves 1951- Verfasser (DE-588)111765560 aut Rational homotopy theory Yves Félix ; Stephen Halperin ; Jean-Claude Thomas New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London Springer 2001 XXXII, 535 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 205 Literaturverz. S. 521 - 530 Rationale Homotopietheorie Homotopy theory Rationale Homotopietheorie (DE-588)4177003-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Rationale Homotopietheorie (DE-588)4177003-1 s DE-604 Homotopietheorie (DE-588)4128142-1 s Halperin, Stephen 1942- Verfasser (DE-588)119201852 aut Thomas, Jean-Claude Verfasser aut Graduate texts in mathematics 205 (DE-604)BV000000067 205 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009323525&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Félix, Yves 1951- Halperin, Stephen 1942- Thomas, Jean-Claude Rational homotopy theory Graduate texts in mathematics Rationale Homotopietheorie Homotopy theory Rationale Homotopietheorie (DE-588)4177003-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4177003-1 (DE-588)4128142-1 |
| title | Rational homotopy theory |
| title_auth | Rational homotopy theory |
| title_exact_search | Rational homotopy theory |
| title_full | Rational homotopy theory Yves Félix ; Stephen Halperin ; Jean-Claude Thomas |
| title_fullStr | Rational homotopy theory Yves Félix ; Stephen Halperin ; Jean-Claude Thomas |
| title_full_unstemmed | Rational homotopy theory Yves Félix ; Stephen Halperin ; Jean-Claude Thomas |
| title_short | Rational homotopy theory |
| title_sort | rational homotopy theory |
| topic | Rationale Homotopietheorie Homotopy theory Rationale Homotopietheorie (DE-588)4177003-1 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Rationale Homotopietheorie Homotopy theory Homotopietheorie |
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| volume_link | (DE-604)BV000000067 |
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