9 problems

Let $M$ be a smooth closed odd-dimensional manifold, let $D$ be its signature operator, and let $\Gamma=\pi_1(M)$ be a torsion-free finitely generated countable discrete group. The…

Mathai's converse conjecture. If $\pi_1(M)$ is torsion-free, then $\rho_{(2)}$ is a homotopy invariant.

Let $M$ be a smooth closed odd-dimensional manifold, let $D$ be its signature operator, and let $\Gamma=\pi_1(M)$ be a torsion-free discrete countable group. The Cheeger-Gromov rho…

Let $M$ be a PL $n$-manifold, let $\Delta(M)$ denote its complexity, and define its sum-stable complexity by … The limit exists by subadditivity. Sum-stable complexity conjecture.…

Let $M$ be a closed manifold with a Riemannian metric whose geometry is bounded, meaning that its dimension, injectivity radius, and sectional curvature satisfy fixed bounds. Suppo…

Fiber-homotopy rho-form conjecture. One should be able to construct and then use rho-forms to distinguish maps that are not fiber diffeomorphic but are fiber homotopy equivalent.

Let $(V,\mathcal F)$ and $(V',\mathcal F')$ be foliated manifolds with holonomy-invariant transverse measures $\Lambda$ and $\Lambda'$, respectively, and let … be a leafwise measur…

Let $\pi\colon M\to B$ and $\theta\colon N\to B$ be smooth fibre bundles of compact manifolds over the same base, with normal $\Gamma$-coverings $p\colon \widetilde M\to M$ and…

Let $\pi\colon M\to B$ be a smooth fibre bundle of compact manifolds, let $p\colon \widetilde M\to M$ be a normal covering with torsion-free deck-transformation group $\Gamma$, and…