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ISSN: 00760552 ISBN: 1139886231 1107100046 1107087848 1107094070 1107102588 1107090970 1107325749 9781107087842 9781107325746 1299707009 9781299707009 0521339464 9780521339469 Year: 1987 Volume: 117 Publisher: Cambridge : Cambridge University Press,
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This 1987 volume presents a collection of papers given at the 1985 Durham Symposium on homotopy theory. They survey recent developments in the subject including localisation and periodicity, computational complexity, and the algebraic K-theory of spaces.
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ISBN: 0511666276 Year: 1953 Publisher: Cambridge : Cambridge University Press,
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Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cell-complexes and their application to homotopy groups of complexes.
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ISBN: 1108912907 1108917275 Year: 2021 Publisher: Cambridge, UK ; New York, NY : Cambridge University Press,
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The long-standing Kervaire invariant problem in homotopy theory arose from geometric and differential topology in the 1960s and was quickly recognised as one of the most important problems in the field. In 2009 the authors of this book announced a solution to the problem, which was published to wide acclaim in a landmark Annals of Mathematics paper. The proof is long and involved, using many sophisticated tools of modern (equivariant) stable homotopy theory that are unfamiliar to non-experts. This book presents the proof together with a full development of all the background material to make it accessible to a graduate student with an elementary algebraic topology knowledge. There are explicit examples of constructions used in solving the problem. Also featuring a motivating history of the problem and numerous conceptual and expository improvements on the proof, this is the definitive account of the resolution of the Kervaire invariant problem.
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ISBN: 1108672671 1108636578 Year: 2020 Publisher: Cambridge : Cambridge University Press,
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The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.
ISBN: 9780821802960 0821802968 Year: 1995 Publisher: Providence (R.I.): American mathematical society,
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Year: 1970 Publisher: Berlin: Springer,
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ISBN: 0821803050 9780821803059 Year: 1995 Publisher: Providence (R.I.): American mathematical society,
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ISBN: 9780821839225 0821839225 Year: 2006 Publisher: Providence (R.I.): American mathematical society,
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ISBN: 0821828010 9780821828014 Year: 2002 Publisher: Providence (R.I.): American mathematical society,
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ISBN: 9780821820780 0821820788 Year: 2000 Publisher: Providence (R.I): American mathematical society,
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