Four-manifolds, Geometries and Knots
by Jonathan Hillman
Publisher: arXiv 2009
Number of pages: 396
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of such manifolds and knots. The first chapter is purely algebraic. The rest of the book may be divided into three parts: general results on homotopy and surgery, geometries and geometric decompositions, and 2-knots.
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by Andrew Ranicki - Springer
This book is an introduction to high-dimensional knot theory. It uses surgery theory to provide a systematic exposition, and it serves as an introduction to algebraic surgery theory, using high-dimensional knots as the geometric motivation.
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This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.
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