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" Stable homotopy around the Arf-Kervaire invariant / "
Victor P. Snaith.
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BL
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| Record Number
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953028
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b707398
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| Main Entry
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Snaith, Victor P., (Victor Percy),1944-
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| Title & Author
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Stable homotopy around the Arf-Kervaire invariant /\ Victor P. Snaith.
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| Publication Statement
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Basel ;Boston :: Birkhäuser,, ©2009.
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| Series Statement
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Progress in mathematics ;; v. 273
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| Page. NO
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1 online resource (xiv, 239 pages) :: illustrations
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| ISBN
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3764399031
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: 376439904X
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: 9783764399030
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: 9783764399047
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| Bibliographies/Indexes
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Includes bibliographical references (pages 217-233), and index.
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| Contents
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Algebraic Topology Background -- The Arf-Kervaire Invariant via QX -- The Upper Triangular Technology -- A Brief Glimpse of Algebraic K-theory -- The Matrix Corresponding to 1??3 -- Real Projective Space -- Hurewicz Images, BP-theory and the Arf-Kervaire Invariant -- Upper Triangular Technology and the Arf-Kervaire Invariant -- Futuristic and Contemporary Stable Homotopy.
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| Abstract
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This book provides a clean, self-contained treatment of a long-standing piece of algebraic topology: the Kervaire invariant one problem. Beginning with the historical background, framing the problem in a stable homotopy theoretical point of view (using work of Browder to recast the geometric problem of manifolds into one of the survival of elements in the Adams spectral sequence), the book quickly moves into more modern approaches, looking at the stable homotopy groups of [italic]BO and then the relationship with the image of [italic]J. The book also makes careful use of the author's "upper triangular technology'', which provides a nice connection between various operations in connective [italic]K-theory and upper triangular 2-adic matrices.
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| Subject
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Homotopy theory.
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Homotopy theory.
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MATHEMATICS-- Topology.
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Homotopy theory.
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| Dewey Classification
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514.24
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| LC Classification
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QA612.7.S63 2009
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| NLM classification
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O189. 23clc
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