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The stable parametrized h-cobordism theorem

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter deals with the stable parametrized h-cobordism theorem. It begins with a discussion of the manifold part; here DIFF is written for the category of Csuperscript infinity smooth manifolds, ... More


On simple maps

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter deals with simple maps of finite simplicial sets, along with some of their formal properties. It begins with a discussion of simple maps of simplicial sets, presenting a proposition for ... More


Introduction

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.003.0001
Subject:
Mathematics, Geometry / Topology

This book presents a proof of the stable parametrized h-cobordism theorem, which deals with the existence of a natural homotopy equivalence for each compact CAT manifold. In this theorem, a stable ... More


An equivalence of categories

Ehud Hrushovski and François Loeser

in Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691161686
eISBN:
9781400881222
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161686.003.0013
Subject:
Mathematics, Geometry / Topology

This chapter deduces from Theorem 11.1.1 an equivalence of categories between a certain homotopy category of definable subsets of quasi-projective varieties over a given valued field and a suitable ... More


Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

Friedhelm Waldhausen, Bjørn Jahren, and John Rognes

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157757
eISBN:
9781400846528
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157757.001.0001
Subject:
Mathematics, Geometry / Topology

Since its introduction by the author 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 ... More


Applications to the topology of Berkovich spaces

Ehud Hrushovski and François Loeser

in Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691161686
eISBN:
9781400881222
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161686.003.0014
Subject:
Mathematics, Geometry / Topology

This chapter presents various applications to the topology of classical Berkovich spaces. It deduces from the main theorem several new results on the topology of V(superscript an) which were not ... More


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