By V. A. Vassiliev
This e-book stories a wide category of topological areas, a lot of which play a huge function in differential and homotopy topology, algebraic geometry, and disaster idea. those comprise areas of Morse and generalized Morse features, iterated loop areas of spheres, areas of braid teams, and areas of knots and hyperlinks. Vassiliev develops a normal approach for the topological research of such areas. one of many primary effects here's a procedure of knot invariants extra strong than all identified polynomial knot invariants. furthermore, a deep relation among topology and complexity conception is used to procure the simplest identified estimate for the numbers of branchings of algorithms for fixing polynomial equations. during this revision, Vassiliev has additional a piece at the fundamentals of the idea and category of adorns, info on purposes of the topology of configuration areas to interpolation conception, and a precis of modern effects approximately finite-order knot invariants. experts in differential and homotopy topology and in complexity idea, in addition to physicists who paintings with string thought and Feynman diagrams, will locate this e-book an updated reference in this fascinating zone of arithmetic.