Abstract
A new method of calculating the topological properties of a polymer chain in the lattice of obstacles on the plane is considered in detail. It is shown that, by applying the method of conformal transformations, it is possible to reduce the problem of calculation of the partition function of the polymer chain in a given topological state with respect to the lattice of obstacles to a much more simple problem of the calculation of the Green function of a free random walk without any topological restrictions on a Riemann surface.
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