High-dimensional Knot Theory
by Andrew Ranicki
Publisher: Springer 1998
Number of pages: 693
This book is devoted entirely to high-dimensional knot theory. It actually has two aims: (1) to serve as an introduction to high-dimensional knot theory, using surgery theory to provide a systematic exposition, (2) to serve as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
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by S.Chmutov, S.Duzhin, J.Mostovoy - Ohio State Universit
An introduction to the theory of finite type (Vassiliev) knot invariants, with a stress on its combinatorial aspects. Written for readers with no background in this area, and we care more about the basic notions than about more advanced material.
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The book gathers together the main strands of the theory of ends of manifolds from the last thirty years and presents a unified and coherent treatment of them. It also contains authoritative expositions of mapping tori and telescopes.
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Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds.