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People have been interested in knots at least since the time of
Alexander the Great and his encounter with the Gordian knot. There
are famous knot illustrations in the Book of Kells and throughout
traditional Islamic art. Lord Kelvin believed that atoms were knots
in the ether and he encouraged Tait to compile a talbe of knots
about 100 years ago. In recent years, the Jones polynomial has
stimulated much interest in possible relationships between knot
theory and physics. The book is concerned with the fundamental
question of the classification of knots, and more generally the
classification of arbitrary (compact) topological objects which can
occur in our normal space of physical reality. Professor Hemion
explains his classification algorithm - using the method of normal
surfaces - in a simple and concise way. The reader is thus shown
the relevance of such traditional mathematical objects as the Klein
bottle or the hyperbolic plane to this basic classification theory.
The Classification of Knots and 3-dimensional Spaces will be of
interest to mathematicians, physicists, and other scientists who
want to apply this basic classification algorithm to their research
in knot theory.
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