6 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…

Semi-splitting conjecture. The deformation of $H^*(M \times N)$ determined by $H^*(E)$ is semi-split with respect to $H^*(M)$. This conjecture proposes a general cohomological spli…

Fibre-wise Morse function conjecture. The theorem holds without the assumption that such a function exists.

Converse signature conjecture. There is a smooth fibre bundle

Fibre-bundle conjecture. Fault-tolerant logical gates can always be expressed as arising from monodromies of an appropriate fibre bundle with a flat projective connection.

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…