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Annals of Mathematics Studies: Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Bjø Jahren, Friedhelm Waldhausen and John Rognes (2013, Trade Paperback)

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SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS (AM-186) (ANNALS OF MATHEMATICS STUDIES (186)) By Friedhelm Waldhausen, Bjorn Jahren, John Rognes **BRAND NEW**.

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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.

Product Identifiers

Publisher
Princeton University Press
ISBN-10
0691157766
ISBN-13
9780691157764
eBay Product ID (ePID)
150582176

Product Key Features

Author
Bjø Jahren, John Rognes, Friedhelm Waldhausen
Publication Name
Spaces of PL Manifolds and Categories of Simple Maps (Am-186)
Format
Trade Paperback
Language
English
Publication Year
2013
Series
Annals of Mathematics Studies
Type
Textbook
Number of Pages
192 Pages

Dimensions

Item Length
9.3in
Item Height
0.4in
Item Width
6.3in
Item Weight
9 Oz

Additional Product Features

Series Volume Number
186
Lc Classification Number
Qa613.4.W35 2013
Reviews
The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology. ---Michael Weiss, Jahresber, "The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology." ---Michael Weiss, Jahresber, "The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology." --Michael Weiss, Jahresber, It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program. ---Bruce Hughes, Zentralblatt MATH, "It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program." --Bruce Hughes, Zentralblatt MATH, "It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program." ---Bruce Hughes, Zentralblatt MATH, "The book has been written with enormous patience but it is not for impatient readers. For me, appreciation came gradually with meditations on the vast historical context of the book and the fascinating pitfalls of combinatorial topology."-- Michael Weiss, Jahresber
Copyright Date
2013
Topic
Geometry / Differential, Functional Analysis, Transformations, Topology
Lccn
2012-038155
Intended Audience
College Audience
Illustrated
Yes
Genre
Mathematics

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item 1 Spaces of PL Manifolds and Categories of Simple Maps (Am-186)
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item 2 SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS By Friedhelm Waldhausen
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item 3 Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Waldhausen: New
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item 6 Spaces Of Pl Manifolds And Categories Of Simple Maps (Am-186)
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Picture 1 of 1

Annals of Mathematics Studies: Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Bjø Jahren, Friedhelm Waldhausen and John Rognes (2013, Trade Paperback)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Spaces of PL Manifolds and Categories of Simple Maps (Am-186)

item 2 SPACES OF PL MANIFOLDS AND CATEGORIES OF SIMPLE MAPS By Friedhelm Waldhausen

item 3 Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Waldhausen: New

item 4 Spaces of PL Manifolds and Categories of Simple Maps, Paperback by Waldhausen...

item 5 Spaces of PL Manifolds and Categories of Simple Maps, Paperback by Waldhausen...

item 6 Spaces Of Pl Manifolds And Categories Of Simple Maps (Am-186)

item 7 Spaces of PL Manifolds and Categories of Simple Maps (AM-186) by Friedhelm Waldh

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Self Heal by Design : The Role of Micro-organisms for Health by Barbara O'Neill (2018, Trade Paperback)

Research Design : Qualitative, Quantitative, and Mixed Methods Approaches by J. David Creswell and John W. Creswell (2022, Trade Paperback)

Designing Data-Intensive Applications : The Big Ideas Behind Reliable, Scalable, and Maintainable Systems by Martin Kleppmann (2017, Trade Paperback)

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