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Ends of Complexes by Bruce Hughes, Andrew Ranicki
 
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Ebooks May 30, 2022 4

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Author
Bruce Hughes, Andrew Ranicki
Publisher
Cambridge University Press 2008
The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. 
Exact Sequences in the Algebraic Theory of Surgery by Andrew Ranicki
 
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Author
Andrew Ranicki
Publisher
Princeton University Press 1981
One of the principal aims of surgery theory is to classify the homotopy types of manifolds using tools from algebra and topology. The algebraic approach is emphasized in this book, and it gives the reader a good overview of the subject, as it was known at the time of...
Geometric Topology: Localization, Periodicity and Galois Symmetry by Dennis Sullivan
 
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Author
Dennis Sullivan
Publisher
Springer 2005
In 1970, Sullivan circulated a set of notes introducing localization and completion of topological spaces to homotopy theory, and other important concepts that have had a
The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds by A.A. Ranicki, et al,
 
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Author
A.A. Ranicki, et al,
Publisher
Springer 1996
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology.
 
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Author
Frank Quinn, Andrew Ranicki
Publisher
2006
Homology manifolds were developed in the first half of the 20th century to give a precise setting for Poincare's ideas on duality. Exotic homology manifolds are
Lower K- and L-theory by Andrew Ranicki
 
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Author
Andrew Ranicki
Publisher
Cambridge University Press 2001
This is the first treatment in book form of the applications of the lower K- and L-groups (which are the components of the Grothendieck groups of modules and quadratic forms over polynomial extension rings)
Noncommutative Localization in Algebra and Topology by Andrew Ranicki
 
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Ebooks May 29, 2022 5

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Author
Andrew Ranicki
Publisher
Cambridge University Press 2002
Noncommutative localization is a powerful algebraic technique for constructing new rings by inverting elements, matrices and more generally morphisms of modules. The applications to topology are via the noncommutative localizations of the fundamental group rings.
Surgery on Compact Manifolds by C.T.C. Wall, A. A. Ranicki
 
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Author
C.T.C. Wall, A. A. Ranicki
Publisher
American Mathematical Society 1999
This book represents an attempt to collect and systematize the methods and main applications of the method of surgery, insofar as compact (but not necessarily connected, simply connected or closed) manifolds are involved.
Algebraic and Geometric Surgery by Andrew Ranicki
 
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Ebooks May 29, 2022 3

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Author
Andrew Ranicki
Publisher
Oxford University Press 2002
This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds.
Algebraic L-theory and Topological Manifolds by A. A. Ranicki
 
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Author
A. A. Ranicki
Publisher
Cambridge University Press 2011
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.
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