A bordism theory related to matrix Grassmannians

Mathematics – Algebraic Topology

Scientific paper

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10 pages

Scientific paper

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.

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