Global knots are knots in 3-manifolds different from the 3-sphere. In contrast to tables of classical knots, which appeared more than two centuries ago, first tables of global knots had been composed only recently. The report is devoted to tabulation of knots in T x I , where T is the 2-dimensional torus. In order to avoid repetitions, we use a new version of the Kauffman polynomial, which is a quantum or state sum invariant of knots in T x I. In contrast to the classical polynomial, which depends on one variable, the new one depends on two variables. We show that all prime knots in T x I having diagrams with 5 or less crossings have different two-variable polynomials. It follows that the table contains no duplicates.
The author is partially supported by Laboratory of Quantum Topology of Chelyabinsk State University (Russian Federation government grant 14.Z50.31.0020).