2-Knots and their Groups

ISBN: 978-0-521-37173-5
Verlag: Cambridge University Press

Buch, Englisch

Reihe: Australian Mathematical Society Lecture Series

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.

Autoren/Hrsg.

Hillman, Jonathan

Inhaltsverzeichnis

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.