by Louis H. Kauffman
Publisher: arXiv 2004
Number of pages: 107
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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by Liviu I. Nicolaescu - World Scientific Publishing Company
An introduction to the most frequently used techniques in modern global geometry. Suited to the beginning graduate student, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.
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This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research.
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This book represents an attempt to collect and systematize the methods and main applications of the method of surgery, insofar as compact (but not necessarily connected, simply connected or closed) manifolds are involved.
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Surgery theory is the standard method for the classification of high-dimensional manifolds, where high means 5 or more. This book aims to be an entry point to surgery theory for a reader who already has some background in topology.