2-Knots and their Groups

To attack certain problems in 4-dimensional knot theory the author draws on a variety of techniques, focusing on knots in S^T4.

Jonathan Hillman (Author)

9780521378123, Cambridge University Press

Paperback, published 30 March 1989

176 pages
22.9 x 15.2 x 1.9 cm, 0.435 kg

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.

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.

Subject Areas: Algebraic topology [PBPD]