Endomorphism K-theory
Endomorphism K-theory is the algebraic K-theory of modules with an endomorphism, such as arise in knot theory via the Seifert matrix.10 An A-module P with an endomorphism f : P → P is essentially the same as a module (P, f) over the polynomial ring A[z],
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Springer-Verlag Berlin Heidelberg GmbH
Andrew Ranicki
High-dimensional Knot Theory Algebraic Surgery in Codimension 2 with an Appendix by Elmar Winkelnkemper
Springer
Andrew Ranicki Department of Mathematics and Statistics University of Edinburgh Edinburgh EH9 3JZ, Scotland, UK Elmar Winkelnkemper Department of Mathematics University of Maryland College Park, MD 20742, USA
The cover design is of a trefoil knot together with a singularity-free spanning surface, that is a Seifert surface. The diagram is taken from the paper of Frankl and Pontrjagin (Math.Ann.l02,785-789 (1930», which proved for the first time that every tame knot k: SI c S3 has a Seifert surface. Library of Congr... Cataloging-in-Publication Data Ranicki, Andrew, 1948High·dimensional knot theory: algebraic surgery in codimension 2 I Andrew Ranicki ; with an appendix by Elmar Winkelnkemper. p. cm. -- (Springer monographs in mathematics) Includes bibliographical references and index.
ISBN 978-3-642-08329-7 ISBN 978-3-662-12011-8 (eBook) DOI 10.1007/978-3-662-12011-8 1. Knot theory 2. Surgery (Topology) 3. Embeddings (Mathematics) 1. Title. Il. Series. QA612.2.R363 1998 514'.224-·dc21 98-25080 CIP
Mathematics Subject Classification (1991): 57Q45, 57R67 ISBN 978-3-642-08329-7
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In memory of J. F. Adams
Preface
On my first day as a graduate student at Cambridge in October, 1970 my official Ph. D. supervisor Frank Adams suggested I work on surgery theory. In September he had attended the International Congress at Nice, where Novikov had been awarded the Fields Medal for his work in surgery. Novikov was prevented by the Soviet authorities from going to the Congress himself, and his lecture on hermitian K-theory [219] was delivered by Mishchenko. As usual, Frank had taken meticulous notes, and presented me with a copy. He also suggested I look at 'Novikov's
