Bibliothèque de L'IMIST/CNRST

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Algebraic homotopy par Baues, Hans Joachim. Publication : [S.l.] Cambridge University Press 1988 . 466 p. , This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra. 24 cm. Date : 1988 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Boundedly controlled topology foundations of algebraic topology and simple homotopy theory par Anderson,, Douglas R. Publication : [S.l.] Springer 2008 . 310 p. , Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Siebenmann's proper simple homotopy theory when Z = IR or IR2. 24 cm. Date : 2008 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Cech and steenrod homotopy theories with applications to geometric topology / par Edwards,, D. A. Publication : [S.l.] : Springer, 1976 . 303 p. ; 24 cm. Date : 1976 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Introduction to homotopy theory par Arkowitz, Martin. Publication : New York Springer 2011 . xiii, 344 pages 24 cm. Date : 2011 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Rational homotopy theory par Félix, Y. Publication : New York Springer 2001 . xxxii, 535 pages 25 cm. Date : 2001 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Rings, modules, and algebras in stable homotopy theory par Elmendorf, A. D. Publication : Providence, R.I. American Mathematical Society 2007 . 249 p. , This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of "$S$-modules" whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of "$S$-algebras" and "commutative $S$-algebras" in terms of associative, or associative and commutative, products $Rwedge _SR longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A_{infty }$ and $E_{infty }$ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $Rwedge _SMlongrightarrow M$. When $R$ is commutative, the category of $R$-modules also has an associative, commutative, and unital smash product, and its derived category has properties just like the stable homotopy category. These constructions allow the importation into stable homotopy theory of a great deal of point-set level algebra. 26 cm. Date : 2007 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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Localization of nilpotent groups and spaces / par Hilton, Peter John. Publication : . 1 online resource (x, 156 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780444107763,  http://www.sciencedirect.com/science/publication?issn=03040208&volume=15,

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Homotopy theory : an introduction to algebraic topology. par Gray, Brayton. Publication : . 1 online resource (xiii, 368 pages) : Disponibilité :  http://www.sciencedirect.com/science/book/9780122960505,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=64,

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Lectures on homotopy theory / par Piccinini, Renzo A., Publication : . 1 online resource (xii, 293 pages) : , An expanded version of lectures given at the Scuola Matematica Interuniversitaria, in Perugia, during the summer of 1989. Disponibilité :  http://www.sciencedirect.com/science/book/9780444892386,  http://www.sciencedirect.com/science/publication?issn=03040208&volume=171,

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Homotopy theory / par Hu, S. T. Publication : . 1 online resource (347 pages) Disponibilité :  http://www.sciencedirect.com/science/book/9780123584502,  http://www.sciencedirect.com/science/publication?issn=00798169&volume=8,

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Categorical constructions in stable homotopy theory : a seminar given at the ETH, Zürich, in 1967 / par Tierney, Myles, Publication : Berlin : Springer-Verlag, 1969 . 65 pages. ; 28 cm. Date : 1969 Disponibilité : Exemplaires disponibles: La bibliothèque des Sciences Exactes et Naturelles (1),

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