10 problems

Honda's conjecture. These contact structures are not symplectically semi-fillable, and hence are not symplectically fillable.

K-contact tight-minimizer conjecture. K-contact structures on $S^1$-bundles always define tight minimizers.

Let $E\to M$ be an orientable circle bundle, and let $\hat{E}\to M$ be another circle bundle. Write $H$ and $\hat{H}$ for the respective T-dual fluxes, and integrate each flux over…

Let $X$ be a compact, acyclic, orientable circle bundle of dimension $n$, and let $k[pi_1(X)]$ denote its fundamental group algebra over a field $k$. A superpotential algebra is an…

Circle-bundle Hopf property conjecture. Every finite-index subgroup of $\pi_1(M)$ is Hopfian for every circle bundle over an aspherical manifold $N$ with hyperbolic $\pi_1(N)$; mor…

Monotone invariant conjecture. In every dimension $n$, there is such a homotopy $n$-manifold numerical invariant $I_n$ that is positive and finite on every circle bundle over a clo…

Let $M$ be the base space of a circle bundle, let $q_0\in M$, and let $s:M-\{q_0\}\to\pi^{-1}(M-\{q_0\})$ be a smooth section extending the section over $U_1$ from the preceding le…

Let $E$ be the total space of a circle bundle over a closed surface $a3_g$ of genus $g\tra 2$, and let $e(E)$ denote its Euler number. A flat conformal structure on $E$ is a confor…

T-duality coset conjecture. Each coset is precisely the collection of $b$-fields with the same T-dual, even when the base space is not simply connected. Thus, modulo the indicated…

Let $M$ be a closed, compact 3-manifold, and let … be a circle bundle with Euler class $e(E)$. Taubes's conjecture. If $E$ is symplectic, then there is a fibration … such that … Th…