LET US CONSIDER A LOOP IN X

A. T. Fomenko, D. B. Fuchs, and V. L. Gutemacher, Homotopic Topology, Akademiaia Kiado, Budapest, 1986

It can be lifted to T. We assign to it the endpoint of the corresponding path in T. (The starting point coincides with * while the endpoint is only known to belong to pi ^-1 (*).)