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Which homology 3-spheres bound homology 4-balls?Ancient/folklore✭✭✭✭0rybu
Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere?Kirby✭✭✭0rybu
What is the homotopy type of the group of diffeomorphisms of the 4-sphere?Smale✭✭✭✭0rybu
Upgrading a completary multifuncoidPorton✭✭0porton
Unsolvability of word problem for 2-knot complementsGordon✭✭✭0rybu
The 4x5 chessboard complex is the complement of a link, which link? David Eppstein✭✭0rybu
Strict inequalities for products of filtersPorton✭0porton
Sticky Cantor sets✭✭0porton
Smooth 4-dimensional Schoenflies problemAlexander✭✭✭✭0rybu
Smooth 4-dimensional Poincare conjecturePoincare; Smale; Stallings✭✭✭✭0rybu
Slice-ribbon problemFox✭✭✭✭0rybu
S(S(f)) = S(f) for reloidsPorton✭✭0porton
Realisation problem for the space of knots in the 3-sphereBudney✭✭0rybu
Rank vs. GenusJohnson✭✭✭0Jesse Johnson
Outer reloid of restricted funcoidPorton✭✭0porton
Nonseparating planar continuum✭✭0porton
Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere?Novikov✭✭✭0rybu
Is every regular paratopological group Tychonoff?unknown✭✭0porton
Inscribed Square ProblemToeplitz✭✭0dlh12
Hilbert-Smith conjectureDavid Hilbert; Paul A. Smith✭✭0porton
Graph product of multifuncoidsPorton✭✭0porton
Fundamental group torsion for subsets of Euclidean 3-spaceAncient/folklore✭✭0rybu
Funcoidal products inside an inward reloidPorton✭✭0porton
Domain and image of inner reloidPorton✭✭0porton
Distributivity of inward reloid over composition of funcoidsPorton✭✭0porton
Composition of reloids expressed through atomic reloidsPorton✭✭0porton
Composition of funcoids expressed through composition of binary relationsPorton✭✭0porton
Closing Lemma for Diffeomorphism (Dynamical Systems)Charles Pugh✭✭✭✭0Jailton Viana
Atomicity of the poset of multifuncoidsPorton✭✭0porton
Atomicity of the poset of completary multifuncoidsPorton✭✭0porton
Jacob Palis Conjecture(Finitude of Attractors)(Dynamical Systems)✭✭✭✭0Jailton Viana

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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