6 problems

Let $M$ be a closed oriented manifold with an effective $S^1$-action. For each connected component $F$ of $M^{S^1}$, assume the hypotheses on $\Gamma_F$, its smooth subalgebra, and…

Let $M^n$ be a closed oriented manifold, with fundamental class $[M]\in H_n(M,\mathbb Z)$ and total $L$-class $\mathcal L(M)\in H^*(M,\mathbb Q)$. Let $\pi$ be a discrete group, le…

Novikov's conjecture. The higher signatures are oriented homotopy invariant. The conjecture is a central problem in index theory and topology. In the paper's setting, it is related…

Let $M$ be a smooth manifold and let $E\subset TM$ be an integrable subbundle defining a foliation $\mathcal{F}$ whose leaves are rationally contractible, meaning that for every le…

Let $(M,\mathcal{F})$ be a foliation on a compact manifold, let $BG$ be the classifying space of its holonomy groupoid, and let $\mathcal{L}^{lf}$ be the cosheaf assigning to each…

Let $(M,\partial M)$ be a compact oriented smooth manifold with boundary, and let $G$ and $\Gamma$ be groups associated to the boundary and manifold through a homomorphism…