By S. K. Nechaev

During this booklet, the writer publicizes the category of difficulties referred to as "entropy of knots" and offers the review of present topological invariants. He constructs statistical versions on braids utilizing the representations of Alexander and Jones invariants and places ahead the query of restrict distribution of those invariants for randomly generated braids. The relation of optimum powers of corresponding algebraic invariants to the Lyapunov exponents of the goods of noncommunicative matrices is proven. additionally the matter of conditional joint restrict distribution for "brownian bridges" on braids is mentioned. certain instances of noncommutative teams PSL(2,R), PSL(2,Z) and braid teams are thought of intimately. within the quantity, the writer additionally discusses the appliance of conformal equipment for the categorical development of topological invariants for random walks on multiconnected manifolds. moreover the relationship of those topological invariants and the monodromy homes of correlation features of a few conformal theories also are mentioned.

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