2 problems

Let $(M,\sigma)$ be a closed connected totally non-spin spin$^c$ manifold with $\dim M=n$, fundamental group $\pi$, and classifying map … Let $L$ be the associated spin$^c$ line bu…

Let $(M,L)$ be a closed spin$^c$ non-spin manifold with $\dim M\geq 5$ and with $\mathcal R^{{\mathrm{gen}+}}(M,L)\neq\emptyset$. Fix a basepoint…