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    Rational Homotopy Theory and Differential Forms

    Posted By: AvaxGenius
    Date: 10 Feb 2025 05:51:31
    Rational Homotopy Theory and Differential Forms

    Rational Homotopy Theory and Differential Forms by Phillip Griffiths , John Morgan
    English | PDF (True) | 2013 | 228 Pages | ISBN : 1461484677 | 1.7 MB

    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 simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented.
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    Algebraic Topology: The Abel Symposium 2007

    Posted By: AvaxGenius
    Date: 27 Jan 2025 04:30:14
    Algebraic Topology: The Abel Symposium 2007

    Algebraic Topology: The Abel Symposium 2007 by Nils Baas, Eric M. Friedlander, Björn Jahren, Paul Arne Østvær
    English | PDF (True) | 2009 | 417 Pages | ISBN : 3642011993 | 4 MB

    The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.
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    Strong Shape and Homology

    Posted By: AvaxGenius
    Date: 28 Sep 2023 13:25:26
    Strong Shape and Homology

    Strong Shape and Homology by Sibe Mardešić
    English | PDF | 2000 | 487 Pages | ISBN : 3540661980 | 40.1 MB

    Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C*-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by polyhedra (ANR's) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes.
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    Computational Homology

    Posted By: AvaxGenius
    Date: 23 Jul 2023 14:43:58
    Computational Homology

    Computational Homology by Tomasz Kaczynski , Konstantin Mischaikow , Marian Mrozek
    English | PDF | 2004 | 487 Pages | ISBN : 0387408533 | 39.1 MB

    Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
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    Homotopy Theory of C*-Algebras

    Posted By: AvaxGenius
    Date: 21 Oct 2022 09:18:56
    Homotopy Theory of C*-Algebras

    Homotopy Theory of C*-Algebras by Paul Arne Østvær
    English | PDF(True) | 2010 | 142 Pages | ISBN : 3034605641 | 1.83 MB

    Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.
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    Topology II Homotopy: and Homology. Classical Manifolds

    Posted By: AvaxGenius
    Date: 19 Sep 2022 16:58:12
    Topology II Homotopy: and Homology. Classical Manifolds

    Topology II Homotopy: and Homology. Classical Manifolds by S. P. Novikov, V. A. Rokhlin
    English | PDF | 2004 | 264 Pages | ISBN : 3540519963 | 26.2 MB

    Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
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    Topology I: General Survey

    Posted By: AvaxGenius
    Date: 19 Sep 2022 03:57:25
    Topology I: General Survey

    Topology I: General Survey by S. P. Novikov
    English | PDF | 1996 | 326 Pages | ISBN : 3540170073 | 27.5 MB

    This book constitutes nothing less than an up-to-date survey of the whole field of topology (with the exception of "general (set-theoretic) topology"), or, in the words of Novikov himself, of what was termed at the end of the 19th century "Analysis Situs", and subsequently diversified into the various subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The book gives an overview of these subfields, beginning with the elements and proceeding right up to the present frontiers of research.
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    "Topology Advanced Topics" ed. by Francisco Bulnes

    Posted By: exLib
    Date: 10 Aug 2022 23:59:58
    "Topology Advanced Topics" ed. by Francisco Bulnes

    "Topology Advanced Topics" ed. by Francisco Bulnes
    ITexLi | 2022 | ISBN: 1803550945 9781803550947 1803550937 9781803550930 1803550953 9781803550954 | 107 pages | PDF | 5 MB

    This book discusses various concepts and theories of topology, including diffeomorphisms, immersions, Hausdorff spaces, cobordisms, homotopy theory, symplectic manifolds, topology of quantum field theory, algebraic varieties, dimension theory, Koszul complexes, continuum theory, and metrizability, among others.
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    Fiber Bundles and Homotopy

    Posted By: ksveta6
    Date: 17 Jan 2022 14:54:37
    Fiber Bundles and Homotopy

    Fiber Bundles and Homotopy by Dai Tamaki
    2021 | ISBN: 9811237999 | English | 350 pages | PDF | 76 MB
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    Topology for Physicists

    Posted By: AvaxGenius
    Date: 17 Oct 2020 22:15:25
    Topology for Physicists

    Topology for Physicists by Albert S. Schwarz
    English | PDF | 1994 | 299 Pages | ISBN : 3642081312 | 32.6 MB

    This volume, written by someone who has made many significant contributions to mathematical physics, not least to the present dialogue between mathematicians and physicists, aims to present some of the basic material in algebraic topology at the level of a fairly sophisticated theoretical physics graduate student.
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    Cohomology of Finite Groups

    Posted By: AvaxGenius
    Date: 17 Oct 2020 22:10:05
    Cohomology of Finite Groups

    Cohomology of Finite Groups by Alejandro Adem
    English | PDF | 1994 | 333 Pages | ISBN : 3662062844 | 25.36 MB

    This book deals with the cohomology of groups, particularly finite ones. His- torically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homological algebra and algebraic K-theory. It arose primar- ily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work of H. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the mean- ings of the low dimensional homology groups of aspace X.
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    Geometric Phases in Classical and Quantum Mechanics

    Posted By: AvaxGenius
    Date: 5 Jul 2020 09:39:44
    Geometric Phases in Classical and Quantum Mechanics

    Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruściński
    English | PDF | 2004 | 346 Pages | ISBN : 081764282X | 22.5 MB

    This work examines the beautiful and important physical concept known as the 'geometric phase,' bringing together different physical phenomena under a unified mathematical and physical scheme.
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