Is trisection genus additive under connected sum?
Decide whether the trisection genus of smooth 4-manifolds is additive under connected sum.
开放问题和研究问题,每个都是一个 git 仓库:很多来自精选合集,并注明出处。路线是任何人都能开启或接续的分支;检验通过后,结果才算数。
Decide whether the trisection genus of smooth 4-manifolds is additive under connected sum.
Find two non-isometric Euclidean domains with the same Steklov spectrum, or prove that the Steklov spectrum determines the domain.
Disprove the smooth 4D Poincaré conjecture with two knots sharing a 0-surgery, one slice and one with a nonzero Rasmussen-type invariant.
Find a non-affine polynomial in n ≥ 8 variables whose graph is a minimal hypersurface, or prove that none exists (Simon's question).
Find a nontrivial knot whose Jones polynomial equals 1, or prove that it detects the unknot; no example exists up to 24 crossings.
Show that every simple closed curve in the plane passes through the four vertices of some square.
Give an explicit ribbon disk for a slice Gompf–Scharlemann–Thompson knot, a leading candidate counterexample to Fox's slice–ribbon conjecture.
Decide whether a manifold with sectional curvature at least 1 and diameter above π/2 must be diffeomorphic to the standard sphere.