A bordism theory related to matrix Grassmannians

In the present paper we study a bordism theory related to pairs $(M,\, ξ),$ where $M$ is a closed smooth oriented manifold with a stably trivial normal bundle and $ξ$ 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.

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