Knots and Surfaces

Knots and Surfaces, 9780198533979 (0198533977), Oxford University Press, 1994

The fascination exerted by interlaced patterns and knotted forms is evident in their use in decorative and symbolic art across the centuries. Knotwork is a distinguishing feature of Celtic art, and the intricate beauty of decorated stonework and illuminated manuscripts such as the Lindisfarne Gospels, the Book of Durrow, and the Book of Kells manifests the technical and creative mastery over knotted forms achieved by Celtic artists before AD 800.

The mathematical theory of knots has a comparatively short history, properly beginning with some remarks of C.F. Gauss and being advanced by Victorian pioneers inspired by Lord Kelvin's vortex theory of atomic structure. Whilst the vortex theory fell by the wayside, knot theory became a flourishing branch of pure mathematics. Recent developments have revealed unexpected connections with the theoretical physics of quantum field theory, reuniting knot theory with physics. One of the aims of this book is to provide the background material so as to make accessible the ideas and discoveries of this challenging and expanding area of mathematical research.

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