Link Theory in Manifolds

1997
ISBN: 978-3-540-63435-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1669, 170 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 289 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kaiser, Uwe

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

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.