Obstructions to the existence of $S^1$-actions. Bordism of ramified coverings

In this article the author proves that the values of the multiplicative genera $A_k$ under discussion, where $k=2,3,\dots$, are obstructions to the existence of nontrivial $S^1$-actions on a unitary manifold whose first Chern class is divisible by $k$. The effective computation of these obstructions is carried out for algebraic manifolds. Simultaneously, formulas for the bordism class of a ramified covering are obtained.
Bibliography: 8 titles.