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.

*"synopsis" may belong to another edition of this title.*

**Friedhelm Waldhausen** is professor emeritus of mathematics at Bielefeld University. **Bjørn Jahren** is professor of mathematics at the University of Oslo. **John Rognes** is professor of mathematics at the University of Oslo.

"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."

*"About this title" may belong to another edition of this title.*

Published by
Princeton University Press
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Princeton University Press, 2013. Hardcover. Book Condition: New. Clean condition, has a mark on the edge of the book, clean pages, hard-bound, Publisher: Princeton University Press. Bookseller Inventory # A-kiwip-06155

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
First Edition
Quantity Available: 1

Seller:

Rating

**Book Description **Princeton University Press, 2013. Hardcover. Book Condition: New. book. Bookseller Inventory # M0691157758

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Quantity Available: 3

Seller:

Rating

**Book Description **Princeton University Press, 2013. HRD. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # WP-9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press, United States
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Princeton University Press, United States, 2013. Hardback. Book Condition: New. New. Language: English . Brand New Book. 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. Bookseller Inventory # AAH9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press, United States
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Princeton University Press, United States, 2013. Hardback. Book Condition: New. New. Language: English . Brand New Book. 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. Bookseller Inventory # AAH9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press 2013-04-28, Princeton
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **Princeton University Press 2013-04-28, Princeton, 2013. hardback. Book Condition: New. Bookseller Inventory # 9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 3

Seller:

Rating

**Book Description **Princeton University Press. Hardback. Book Condition: new. BRAND NEW, Spaces of PL Manifolds and Categories of Simple Maps, Friedhelm Waldhausen, Bjorn Jahren, John Rognes, 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. Bookseller Inventory # B9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton University Press, United States
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 10

Seller:

Rating

**Book Description **Princeton University Press, United States, 2013. Hardback. Book Condition: New. New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. Bookseller Inventory # BTE9780691157757

More Information About This Seller | Ask Bookseller a Question

Published by
Princeton Univ Pr
(2013)

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 2

Seller:

Rating

**Book Description **Princeton Univ Pr, 2013. Hardcover. Book Condition: Brand New. 184 pages. 9.50x6.25x0.50 inches. In Stock. Bookseller Inventory # __0691157758

More Information About This Seller | Ask Bookseller a Question

ISBN 10: 0691157758
ISBN 13: 9780691157757

New
Hardcover
Quantity Available: 1

Seller:

Rating

**Book Description **2013. Hardback. Book Condition: NEW. 9780691157757 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Bookseller Inventory # HTANDREE01147322

More Information About This Seller | Ask Bookseller a Question