A bordism theory related to matrix Grassmannians

Abstract

In the present paper we study a bordism theory related to pairs $(M,\, \xi),$ where $M$ is a closed smooth oriented manifold with a stably trivial normal bundle and $\xi$ is a virtual $\SU$-bundle of virtual dimension 1 over $M$. The main result is the calculation of the corresponding ring modulo torsion and the explicit description of its generators.