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1992; 60 minutes; DVD
List Price: US$25
Order Code: DVD/77
Temporarily out of stock.
Expected date of availability is July 1, 2013.
This lecture provides an excellent introduction to knot theory. Taking an intuitive, pictorial approach, Cappell describes some of the deep connections between knots and some fairly abstract mathematics. The lecture begins at the beginning, with basic definitions clearly laid out. Cappell shows how the technique of coloring different segments of knots provides a simple way to bring in some of the main ideas of the subject. He notes that knots naturally arise when one looks at polynomial equations, pointing out that knot theory provides the simplest case in which one can examine the topology of complex varieties. Moving on to a discussion of surgery and knot complements, he connects the discussion to branched coverings, which seem to hold a tantalizing key to describing all three-manifolds. Cappell's lucid, energetic lecture style keeps the presentation moving at just the right pace. This DVD would provide a fine introduction to the subject for an audience of undergraduate mathematics majors.
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