Algebraic L-theory and Topological Manifolds


Author: A. A. Ranicki
Publisher: Cambridge University Press
ISBN: 9780521420242
Category: Mathematics
Page: 358
View: 6833
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Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.

Automorphisms of Manifolds and Algebraic K-Theory: Part III


Author: Michael S. Weiss, Bruce E. Williams
Publisher: American Mathematical Soc.
ISBN: 147040981X
Category: Mathematics
Page: 110
View: 6779
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The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

Lower K- and L-theory


Author: Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521438018
Category: Mathematics
Page: 174
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This is the first unified treatment in book form of the lower K-groups of Bass and the lower L-groups of the author.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Oberwolfach 1993
Author: Steven C. Ferry
Publisher: Cambridge University Press
ISBN: 9780521497961
Category: Mathematics
Page: 384
View: 3078
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The Novikov conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes give a snapshot of the status of work on the Novikov conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, and analysis. Volume 1 contains a detailed historical survey and bibliography of the Novikov conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; an annotated problem list; the texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and research/survey papers on the Novikov conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg. Volume 2 contains fundamental long research papers by G. Carlsson on "Bounded K-theory and the assembly map in algebraic K-theory" and by S. Ferry and E. Pedersen on "Epsilon surgery theory"; and shorter research and survey papers on various topics related to the Novikov conjecture, by Bekka, Cherix, Valette, Eichhorn, and others. These volumes will appeal to researchers interested in learning more about this intriguing area.

High-dimensional Knot Theory

Algebraic Surgery in Codimension 2
Author: Andrew Ranicki
Publisher: Springer Science & Business Media
ISBN: 3662120119
Category: Mathematics
Page: 646
View: 8198
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Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.

Schriftenreihe des Mathematischen Instituts der Universität Münster


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6119
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Bulletin of the Belgian Mathematical Society, Simon Stevin


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 8951
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London Mathematical Society lecture note series


Author: Andrew Ranicki
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 8256
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Bulletin (new Series) of the American Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 6084
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Algebraic and Geometric Topology


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Algebraic topology
Page: N.A
View: 333
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Documenta Mathematica

Journal Der Deutschen Mathematiker-Vereinigung
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9130
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Sūgaku Expositions

A Translation of Sūgaku
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9483
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Surveys on Surgery Theory

Papers Dedicated to C.T.C. Wall
Author: Sylvain F. Cappell,Sylvain E. Cappell,Andrew Ranicki,Charles Terence Clegg Wall,Jonathan Rosenberg
Publisher: Annals of Mathematics Studies
ISBN: 9780691049380
Category: Mathematics
Page: 448
View: 4514
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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. There have been some extraordinary accomplishments in that time, which have led to enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source that surveys surgery theory and its applications. Indeed, no one person could write such a survey. The sixtieth birthday of C. T. C. Wall, one of the leaders of the founding generation of surgery theory, provided an opportunity to rectify the situation and produce a comprehensive book on the subject. Experts have written state-of-the-art reports that will be of broad interest to all those interested in topology, not only graduate students and mathematicians, but mathematical physicists as well. Contributors include J. Milnor, S. Novikov, W. Browder, T. Lance, E. Brown, M. Kreck, J. Klein, M. Davis, J. Davis, I. Hambleton, L. Taylor, C. Stark, E. Pedersen, W. Mio, J. Levine, K. Orr, J. Roe, J. Milgram, and C. Thomas.

Third International Congress of Chinese Mathematicians


Author: Ka-Sing Lau,Zhouping Xin,Shing-Tung Yau
Publisher: Amer Mathematical Society
ISBN: N.A
Category: Mathematics
Page: 874
View: 2188
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This volume consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics.

Mappings and dimension


Author: V. I. Arnold
Publisher: N.A
ISBN: N.A
Category: Dimension theory (Topology)
Page: 229
View: 2723
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Vorlesungen Über die Zahlentheorie der Quaternionen


Author: Adolf Hurwitz
Publisher: Springer-Verlag
ISBN: 3642475361
Category: Mathematics
Page: 76
View: 531
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Bulletin of the American Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 5313
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Ends of Complexes


Author: Bruce Hughes,Andrew Ranicki
Publisher: Cambridge University Press
ISBN: 9780521576253
Category: Mathematics
Page: 353
View: 4333
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A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.

Marcel Reich-Ranicki


Author: Volker Hage,Mathias Schreiber
Publisher: Kiepenheuer & Witsch
ISBN: 3462412434
Category: Biography & Autobiography
Page: 266
View: 6341
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Marcel Reich-Ranicki, populärster Literaturkritiker Deutschlands, brillierte als »Anwalt der schönen Literatur«, als »Herr der Bücher«.In diesem erstmals 1995 erschienenen Buch von Volker Hage und Mathias Schreiber wird ein größeres biographisches Porträt vorgelegt, ergänzt um zwei Interviews und eine 1958 geschriebene autobiographische Erzählung Reich-Ranickis.

Lehrbuch der Topologie


Author: Herbert Seifert,William Threlfall
Publisher: University of Pennsylvania Press
ISBN: 9780821835951
Category: Mathematics
Page: 353
View: 6228
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The 1930s were important years in the development of modern topology, pushed forward by the appearance of a few pivotal books, of which this is one. The focus is on combinatorial and algebraic topology, with as much point-set topology as needed for the main topics. One sees from the modern point of view that the authors are working in a category of spaces that includes locally finite simplicial complexes. (Their definition of manifold is more properly known today as a ""triangulizable homology manifold"".)Amazingly, they manage to accomplish a lot without the convenient tools of homological algebra, such as exact sequences and commutative diagrams, that were developed later. The main topics covered are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), local homology, surface topology, the fundamental group and covering spaces, three-manifolds, Poincare duality, and the Lefschetz fixed point theorem. Few prerequisites are necessary. A final section reviews the lemmas and theorems from group theory that are needed in the text. As stated in the introduction to the important book by Alexandroff and Hopf (which appeared a year after ""Seifert and Threlfall""): 'Its lively and instructive presentation makes this book particularly suitable as an introduction or as a textbook.'