By Louis H. Kauffman

This quantity offers an advent to knot and hyperlink invariants as generalized amplitudes for a quasi-physical technique. The calls for of knot concept, coupled with a quantum-statistical framework, create a context that clearly features a variety of interrelated issues in topology and mathematical physics. the writer takes a basically combinatorial stance towards knot conception and its family with those matters. This stance has the benefit of supplying direct entry to the algebra and to the combinatorial topology, in addition to actual rules. The ebook is split into components: half 1 is a scientific path on knots and physics ranging from the floor up; and half 2 is a suite of lectures on a variety of issues concerning half 1. half 2 comprises issues resembling frictional houses of knots, family members with combinatorics and knots in dynamical structures. during this 3rd variation, a paper by means of the writer entitled "Knot thought and sensible Integration" has been further. This paper indicates how the Kontsevich vital method of the Vassiliev invariants is at once concerning the perturbative enlargement of Witten's sensible necessary. whereas the ebook offers the historical past, this paper could be learn independently as an advent to quantum box conception and knot invariants and their relation to quantum gravity. As within the moment variation, there's a collection of papers by way of the writer on the finish of the publication. various clarifying comments were additional to the textual content.

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