Manchester Geometry Seminar 2000/2001

For any stably almost complex manifold M we can construct several stably almost complex manifolds canonically related with the original one. These are so called virtual Chern submanifolds which realize Chern classes of the tangent bundle of M in complex cobordism. As a generalization of the classical Milnor--Hirzebruch problem, Buchstaber and Veselov in [1] posed a question to describe all divisibility relations between Chern numbers of a stably complex manifold and its virtual Chern submanifolds. In the present talk we give a complete solution to this problem. We present the formula which allows one to obtain expression for any Chern number of any virtual Chern submanifold in terms of Chern numbers of the original manifold

Reference:

1. V.M.Buchstaber, A.P.Veselov. On a remarkable functional equation in the theory of generalized Dunkl operators and transformations of elliptic genera, Math. Zeitschr. 223 (1996), 595-607.