Twisted Spin cobordism and positive scalar curvature

Understand

We show how a suitably twisted Spin-cobordism spectrum connects to the question of existence of metrics of positive scalar curvature on closed, smooth manifolds by building on fundamental work of Gromov, Lawson, Rosenberg, Stolz and others.

• We then investigate this parametrised spectrum, compute its $mod~2$-cohomology and generalise the Anderson-Brown-Peterson splitting of the regular Spin-cobordism spectrum to the twisted case.
• Along the way we also describe the $mod~2$-cohomology of various twisted, connective covers of real K-theory.