3 problems

Let $F^{2m} \to E \to B^{2n}$ be a fibration of oriented Poincaré complexes, and suppose that the action of $\pi_1(B)$ on $H^{m}(F;\mathbb Z_2)$ is trivial. Klaus–Teichner's conjec…

Let $M$ be a manifold with a proper action of a discrete group $G$, let $\mathcal{A}$ be a $C^{*}$-algebra, and let $\eta_{\mathcal{A}}\in\operatorname{Vect}(M/G;\mathcal{A})$ and…

Hirzebruch formula conjecture. The signature satisfies