2-Knots and Their Groups

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CUP Archive, Mar 30, 1989 - Mathematics - 164 pages
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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.
 

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Contents

Knots and Related Manifolds
1
The Knot Group
15
Localization and Asphericity
36
The Rank 1 Case
52
The Rank 2 Case
70
Ascending Series and the Large Rank Cases
85
The Homotopy Type of MK
107
Applying Surgery to Determine the Knot
124
Appendix A FourDimensional Geometries and Smooth Knots
142
Appendix B Reflexive CappellShaneson 2Knots
145
Some Open Questions I1?
147
References
150
Index
164
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