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000756224 019__ $$a952973269
000756224 020__ $$a9783319234885$$q(electronic book)
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000756224 0247_ $$a10.1007/978-3-319-23488-5$$2doi
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000756224 1001_ $$aFomenko, A. T.,$$eauthor.
000756224 24510 $$aHomotopical topology$$h[electronic resource] /$$cAnatoly Fomenko, Dmitry Fuchs.
000756224 250__ $$aSecond edition.
000756224 264_1 $$aSwitzerland :$$bSpringer,$$c2016.
000756224 300__ $$a1 online resource (xi, 627 pages) :$$billustrations.
000756224 336__ $$atext$$btxt$$2rdacontent
000756224 337__ $$acomputer$$bc$$2rdamedia
000756224 338__ $$aonline resource$$bcr$$2rdacarrier
000756224 4901_ $$aGraduate texts in mathematics,$$x0072-5285 ;$$v273
000756224 504__ $$aIncludes bibliographical references and indexes.
000756224 5050_ $$aIntroduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories.
000756224 506__ $$aAccess limited to authorized users.
000756224 520__ $$aThis classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics--the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra--the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology--the Adams conjecture, Bott periodicity, the Hirzebruch-Riemann-Roch theorem, the Atiyah-Singer index theorem, to name a few--paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role in mathematics, and therefore in the presentation of this book, as well. A judicious focus on the key ideas, at an appropriate magnification of detail, enables the reader to navigate the breadth of material, confidently, without the disorientation of algebraic minutiae. Many exercises are integrated throughout the text to build up the reader's mastery of concepts and techniques. Numerous technical illustrations elucidate geometric constructions and the mechanics of spectral sequences and other sophisticated methods. Over fifty hauntingly captivating images by A. T. Fomenko artistically render the wondrous beauty, and mystery, of the subject.
000756224 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 5, 2016).
000756224 650_0 $$aHomotopy theory.
000756224 650_0 $$aTopological algebras.
000756224 7001_ $$aFuks, D. B.,$$eauthor.
000756224 77608 $$iPrint version:$$z9783319234878
000756224 830_0 $$aGraduate texts in mathematics ;$$v273.
000756224 852__ $$bebk
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