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  3. Locally Flat Embeddings of 3-Manifolds in S4
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  • Publisher:
    Cambridge University Press
    Publication date:
    09 May 2026
    04 June 2026
    ISBN:
    9781009715355
    9781009715386
    DOI:
    https://doi.org/10.1017/9781009715355
    Dimensions:
    Weight & Pages:
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.262kg, 172 Pages
    • Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Australian Mathematical Society Lecture Series (29)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology, Algebra
    Series:
    Australian Mathematical Society Lecture Series (29)
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    Book description

    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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