EAN: 9780387982540

AN INTRODUCTION TO KNOT THEORY - WBRAYMOND LICK...

This volume is an introduction to mathematical Knot Theory  the theory of knots and links of
simple closed curves in three-dimensional space. It consists of a selection of topics which
graduate students have found to be a successful introduction to the field. Three distinct
techniques are employed  Geometric Topology Manoeuvres  Combinatorics  and Algebraic Topology.
Each topic is developed until significant results are achieved and chapters end with exercises
and brief accounts of state-of-the-art research. What may reasonably be referred to as Knot
Theory has expanded enormously over the last decade and while the author describes important
discoveries throughout the twentienth century  the latest discoveries such as quantum
invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial
are also included  presented in an easily understandable style. Thus this constitutes a
comprehensive introduction to the field  presenting modern developments in the context of
classical material. Readers are assumed to have knowledge of the basic ideas of the fundamental
group and simple homology theory although explanations throughout the text are plentiful and
well-done. Written by an internationally known expert in the field  this volume will appeal to
graduate students  mathematicians and physicists with a mathematical background who wish to
gain new insights in this area.

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