Any topological theory of knots and links should be based on simple ideas of intersection and linking. In this book, a general theory of link bordism in manifolds and universal constructions of linking numbers in oriented 3-manifolds are developed. In this way, classical concepts of link theory in the 3-spheres are generalized to a certain class of oriented 3-manifolds (submanifolds of rational homology 3-spheres). The techniques needed are described in the book but basic knowledge in topology and algebra is assumed. The book should be of interst to those working in topology, in particular knot theory and low-dimensional topology.

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Bibliographic Information

Book Title: Link Theory in Manifolds
Authors: Uwe Kaiser
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0092686
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1997
Softcover ISBN: 978-3-540-63435-5Published: 18 September 1997
eBook ISBN: 978-3-540-69546-2Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 170
Topics: Algebraic Topology, Manifolds and Cell Complexes (incl. Diff.Topology), Topology

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Table of contents (7 chapters)

Front Matter

Link bordism in manifolds

Enumeration of link bordism in 3-manifolds

Linking number maps

Surface structures for links in 3-manifolds

Link invariants in Betti-trivial 3-manifolds

Link characteristic and band-operations in Betti-trivial 3-manifolds

3-dimensional Betti-trivial submanifolds

Back Matter

About this book