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Braid and Knot Theory in Dimension Four

By (author) Seiichi Kamada

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Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it to study surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given This book contains a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method are studied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials.

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The Ballerina and the Bull: Anarchist Utopias in the Age of Finance

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Paperback / softback
288 pages
was: R 306.95
now: R 275.95
This title will take longer to obtain, and should be delivered in 6-8 weeks

Our moment has seen the resurgence of an anarchist sensibility, from the uprisings in Seattle in 1999 to the Occupy movement of 2011.

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Fifteen Dogs

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Paperback / softback
176 pages
was: R 280.95
now: R 252.95
Available from overseas. Dispatched in aprox 4-8 weeks as local supplier is out of stock

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Bonsai Success in Southern Africa

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Paperback / softback
160 pages
was: R 320.95
now: R 288.95
Stock is usually dispatched in 6-12 days from date of order

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