Robion C. Kirby's Books

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

By: Robion C. Kirby,Laurence C. Siebenmann

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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

By: Robion C. Kirby,Laurence C. Siebenmann

Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

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Page Count

368

Publisher

Princeton University Press

Published Date

ISBN 10

1400881501

ISBN 13

9781400881505

Handlebody Decompositions of Complex Surfaces

By: John Harer,Arnold Kas,Robion C. Kirby

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Handlebody Decompositions of Complex Surfaces

By: John Harer,Arnold Kas,Robion C. Kirby

This monograph gives framed link pictures of the Kummer surface (= [italic]V4) and some Dolgachev surfaces. The emphasis here is to use the elliptic pencil structure to describe the framed links. This approach is particularly convenient to see the change of handlebody structures of elliptic surfaces after an operation of logarithmic transform, which is an important ingredient in constructing Dolgachev surfaces.

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Page Count

110

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821823515

ISBN 13

9780821823514

The Topology of 4-Manifolds

By: Robion C. Kirby

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The Topology of 4-Manifolds

By: Robion C. Kirby

This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

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Page Count

114

Publisher

Springer

Published Date

ISBN 10

354046171X

ISBN 13

9783540461715

Book's by Robion C. Kirby

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Handlebody Decompositions of Complex Surfaces

Handlebody Decompositions of Complex Surfaces

The Topology of 4-Manifolds

The Topology of 4-Manifolds

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