spaces of pl manifolds and categories of simple maps am 186

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Spaces Of Pl Manifolds And Categories Of Simple Maps Am 186

Author : Friedhelm Waldhausen
ISBN : 9781400846528
Genre : Mathematics
File Size : 63. 95 MB
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Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a "desingularization," improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.

Surveys On Surgery Theory Am 149 Volume 2

Author : Sylvain Cappell
ISBN : 9781400865215
Genre : Mathematics
File Size : 53. 55 MB
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Surgery theory, the basis for the classification theory of manifolds, is now about forty years old. The sixtieth birthday (on December 14, 1996) of C.T.C. Wall, a leading member of the subject's founding generation, led the editors of this volume to reflect on the extraordinary accomplishments of surgery theory as well as its current enormously varied interactions with algebra, analysis, and geometry. Workers in many of these areas have often lamented the lack of a single source surveying surgery theory and its applications. Because no one person could write such a survey, the editors asked a variety of experts to report on the areas of current interest. This is the second of two volumes resulting from that collective effort. It will be useful to topologists, to other interested researchers, and to advanced students. The topics covered include current applications of surgery, Wall's finiteness obstruction, algebraic surgery, automorphisms and embeddings of manifolds, surgery theoretic methods for the study of group actions and stratified spaces, metrics of positive scalar curvature, and surgery in dimension four. In addition to the editors, the contributors are S. Ferry, M. Weiss, B. Williams, T. Goodwillie, J. Klein, S. Weinberger, B. Hughes, S. Stolz, R. Kirby, L. Taylor, and F. Quinn.

Orthogonal Polynomials And Their Applications

Author : Manuel Alfaro
ISBN : 9783540392958
Genre : Mathematics
File Size : 28. 32 MB
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The Segovia meeting set out to stimulate an intensive exchange of ideas between experts in the area of orthogonal polynomials and its applications, to present recent research results and to reinforce the scientific and human relations among the increasingly international community working in orthogonal polynomials. This volume contains original research papers as well as survey papers about fundamental questions in the field (Nevai, Rakhmanov & López) and its relationship with other fields such as group theory (Koornwinder), Padé approximation (Brezinski), differential equations (Krall, Littlejohn) and numerical methods (Rivlin).

Stochastic Mechanics And Stochastic Processes

Author : Aubrey Truman
ISBN : 9783540458876
Genre : Mathematics
File Size : 33. 58 MB
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The main theme of the meeting was to illustrate the use of stochastic processes in the study of topological problems in quantum physics and statistical mechanics. Much discussion of current problems was generated and there was a considerable amount of interaction between mathematicians and physicists. The papers presented in the proceedings are essentially of a research nature but some (Lewis, Hudson) are introductions or surveys.

Surgery On Compact Manifolds

Author : Charles Terence Clegg Wall
ISBN : 9780821809426
Genre : Mathematics
File Size : 65. 14 MB
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The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.

Mathematical Reviews

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ISBN : UOM:39015076649915
Genre : Mathematics
File Size : 59. 36 MB
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Mathematical Logic And Applications

Author : Juichi Shinoda
ISBN : STANFORD:36105032487618
Genre : Mathematics
File Size : 82. 74 MB
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This useful volume adopts a balanced approach between technology and mathematical modeling in computer networks, covering such topics as switching elements and fabrics, Ethernet, and ALOHA design. Examples at the end of each chapter provide ample material for practice.

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