November 18, 1997 S.~S.~Anisov Topological complexity of $T^2$-bundles over $S^1$ and continued fractions This (joint with S.~K.~Lando) work is an attempt to extend Kazarian's method of ``computing the singularities'' to fiber bundles of dimension greater than one. A torus can be represented as a $CW$-complex with two vertices and three edges. These edges form a {\it net}. If the length of one of its edges vanishes, the {\it flip\/} occurs, and the corresponding fiber of the torus bundle over $S^1$ is said to be {\it degenerate}. We show that the algebraic number of degenerate fibers is an invariant of the bundle, i.e., does not depend on the choice of an embedding of the net. We also give an expression for this number in terms of the denominators of a certain continued fraction related to the bundle.