Partially framed manifolds and loop spaces on the group

Chern-Dold character in complex cobordisms and theta divisors

“…They can be expressed through the usual Chern numbers c ω (M 2n ) and contain the same information about U -manifold M 2n . We will use the following convenient class of U -manifolds from [7]. Let M 2n be a smooth real manifold of dimension 2n.…”

“…Since the cohomology groups of Θ n have no torsion [13], this defines them uniquely, but multiplication structure seems still to be understood. that the signature τ (Θ n ) for even n has been computed in [7]:…”