4 problems

Let $M$ be a Riemannian $4k$-manifold with positive Ricci curvature that admits a string structure, meaning that the classifying map of its tangent bundle lifts from…

Let $K$ be a Lie group and let $P_K:M\to\mathrm{B}K$ classify a principal $K$-bundle. Let $\mathrm{B}^2\mathrm{U}(1)\to\mathrm{String}(K)\to K$ be the string extension, enhanced to…

Let $(M_{8\ell+2},g_M^{\mathrm{spin}})$ be a closed differential spin manifold, and let $g_M^{\mathrm{string}}$ be a lift of its spin structure to a differential string structure.…

A string datum consists of local data whose underlying bundle is a principal $\operatorname{Spin}(n)$-bundle $\bar{P}$. Gluing these local data is expected to produce an $S^1$-gerb…