2-Knots and their Groups

by Jonathan Hillman

Overview

To attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S T4, whose fundamental groups contain abelian normal subgroups. Their class contains the most geometrically appealing and best understood examples. Moreover, it is possible to apply work in algebraic methods to these problems. Work in four-dimensional topology is applied in later chapters to the problem of classifying 2-knots.

Product Details

ISBN-13:	9780521378123
Publisher:	Cambridge University Press
Publication date:	03/30/1989
Series:	Australian Mathematical Society Lecture Series , #5
Pages:	176
Product dimensions:	5.98(w) x 9.02(h) x 0.75(d)

Table of Contents

1. Knots and Related Manifolds; 2. The Knot Group; 3. Localization and Asphericity; 4. The Rank 1 Case; 5. The Rank 2 Case; 6. Ascending Series and the Large Rank Cases; 7. The Homotopy Type of M(K); 8. Applying Surgery to Determine the Knot.

Editorial Reviews

To attack certain problems in four-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S4, whose fundamental groups contain abelian normal subgroups. New work in four- dimensional topology is applied to the problem of classifying 2-knots. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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