Spaces of PL Manifolds and Categories of Simple Maps (AM-186) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spaces of PL Manifolds and Categories of Simple Maps (AM-186) write by Friedhelm Waldhausen. This book was released on 2013-04-21. Spaces of PL Manifolds and Categories of Simple Maps (AM-186) available in PDF, EPUB and Kindle. 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.
Spaces of PL Manifolds and Categories of Simple Maps
Spaces of PL Manifolds and Categories of Simple Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spaces of PL Manifolds and Categories of Simple Maps write by Friedhelm Waldhausen. This book was released on 1940. Spaces of PL Manifolds and Categories of Simple Maps available in PDF, EPUB and Kindle.
Spaces of PL Manifolds and Categories of Simple Maps
Spaces of PL Manifolds and Categories of Simple Maps - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spaces of PL Manifolds and Categories of Simple Maps write by Friedhelm Waldhausen. This book was released on 2013-04-28. Spaces of PL Manifolds and Categories of Simple Maps available in PDF, EPUB and Kindle. 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
Surveys on Surgery Theory (AM-149), Volume 2 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Surveys on Surgery Theory (AM-149), Volume 2 write by Sylvain Cappell. This book was released on 2014-09-08. Surveys on Surgery Theory (AM-149), Volume 2 available in PDF, EPUB and Kindle. 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.
Current Trends in Algebraic Topology
Current Trends in Algebraic Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Current Trends in Algebraic Topology write by Richard M. Kane. This book was released on 1982-01-01. Current Trends in Algebraic Topology available in PDF, EPUB and Kindle. Proceedings of a Conference held at the University of Western Ontario in 1981. More than one hundred papers were presented by researchers from a wide spectrum of countries and institutions.
