The study of smooth embeddings of 3-manifolds in 4-space has been hampered by difficulties with the simplest case, that of homology spheres. This book presents some advantages of working with locally flat embeddings. The first two chapters outline the tools used and give general results on embeddings of 3-manifolds in S4. The next two chapters consider which Seifert manifolds may embed, with criteria in terms of Seifert data. After summarizing results on those Seifert manifolds that embed smoothly, the following chapters determine which 3-manifolds with virtually solvable fundamental groups embed. The final three chapters study the complementary regions. When these have 'good' fundamental groups, topological surgery may be used to find homeomorphisms. Figures throughout help illustrate links representing embeddings and open questions are further discussed in the appendices, making this a valuable resource for graduate students and research workers in geometric topology.
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ISBN-13
978-1-009-71538-6 (9781009715386)
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Schweitzer Klassifikation
Jonathan Hillman is an Honorary Associate in the School of Mathematics and Statistics at the University of Sydney. Although an algebraist by nature, he works primarily in low-dimensional topology, and has authored books on links in S3, 2-knots, geometric 4-manifolds and PD3-complexes. His previous books with Cambridge University Press include '2-knots and their Groups' (1989) and 'The Algebraic Characterization of Geometric 4-Manifolds' (1994).
Autor*in
University of Sydney
1. Preliminaries; 2. Invariants and constructions; 3. 3-manifolds with S1-actions; 4. Seifert manifolds with non-orientable base orbifolds; 5. Smooth embeddings; 6. 3-manifolds with restrained fundamental group; 7. The complementary regions; 8. Abelian embeddings; 9. Nilpotent embeddings; Appendix A. The linking pairings of orientable Seifert manifolds; Appendix B. Homologically balanced nilpotent groups; Appendix C. Some questions; References; Index.
