Geometric constructions of bordism between stably complex manifolds and their applications

The formal group of geometric cobordism was introduced In S.P.Novikov's paper (1967), (see Appendix I, A.S.Mischenko's theorem therein). This formal group yields the multiplication law in the universal formal group (D.Quillen's theorem, 1969). The multiplication law in the geometric cobordism formal group was obtained by V.M.Buchstaber (1970). It is straight-forward to deduce the formula for the logarithm of the universal formal group from the Buchstaber's formula and from bordism between Milnor hypersurface H_{1,n} and the Cartesian product CP^1x CP^{n-1}. It is natural to ask for an explicit construction of this bordism. Two explicit constructions of the desired bordism proposed by the author (2018) will be presented in the talk. The first construction relies on the B.Totaro's approach to Hirzebruch genera of singular varieties (2000). The second one uses S.Sarkar's results on bordism of orbifolds with quasitoric boundary (2015). During the talk we will remind the basics of complex bordism theory.