000 04641nam a22005897a 4500
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020 _a9781461484684
_9978-1-4614-8468-4
024 7 _a10.1007/978-1-4614-8468-4
_2doi
050 4 _aQA612-612.8
072 7 _aPBPD
_2bicssc
072 7 _aMAT038000
_2bisacsh
082 0 4 _a514.2
_223
100 1 _aGriffiths, Phillip.
_eauthor.
245 1 0 _aRational Homotopy Theory and Differential Forms
_h[electronic resource] /
_cby Phillip Griffiths, John Morgan.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Birkhäuser,
_c2013.
300 _aXI, 227 p. 46 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x0743-1643 ;
_v16
505 0 _a1 Introduction -- 2 Basic Concepts -- 3 CW Homology Theorem -- 4 The Whitehead Theorem and the Hurewicz Theorem.-  5 Spectral Sequence of a Fibration -- 6 Obstruction Theory -- 7 Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations -- 8 Postnikov Towers and Rational Homotopy Theory -- 9 deRham's theorem for simplicial complexes -- 10 Differential Graded Algebras -- 11 Homotopy Theory of DGAs -- 12 DGAs and Rational Homotopy Theory -- 13 The Fundamental Group -- 14 Examples and Computations -- 15 Functorality -- 16 The Hirsch Lemma -- 17 Quillen's work on Rational Homotopy Theory -- 18 A1-structures and C1-structures -- 19 Exercises.
520 _a“Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now… The appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature.” —Zentralblatt MATH (Review of First Edition)   “The monograph is intended as an introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty of examples, illustrations, diagrams and exercises. The material is developed with patience and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and its power are elegantly presented. This is an excellent monograph.” —Bulletin of the American Mathematical Society (Review of First Edition)   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 Tham’s theorem on simplical complexes. In addition, Sullivan’s 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.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aCategory theory (Mathematics).
650 0 _aHomological algebra.
650 0 _aCommutative algebra.
650 0 _aCommutative rings.
650 0 _aTopology.
650 0 _aAlgebraic topology.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Topology.
650 2 4 _aCategory Theory, Homological Algebra.
650 2 4 _aCommutative Rings and Algebras.
650 2 4 _aTopology.
650 2 4 _aAlgebra.
700 1 _aMorgan, John.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461484677
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v16
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8468-4
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45021
_d45021