MSC2020 · 57Kxx

Low-dimensional topology in specific dimensions

9 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

57K10Knot theory3 57K12Generalized knots (virtual knots, welded knots, quandles, etc.)0 57K14Knot polynomials1 57K16Finite-type and quantum invariants, topological quantum field theories (TQFT)0 57K18Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.)0 57K202-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.)0 57K30General topology of 3-manifolds0 57K31Invariants of 3-manifolds (including skein modules, character varieties)4 57K32Hyperbolic 3-manifolds0 57K33Contact structures in 3 dimensions0 57K35Other geometric structures on 3-manifolds0 57K40General topology of 4-manifolds1 57K41Invariants of 4-manifolds (including Donaldson and Seiberg-Witten invariants)0 57K43Symplectic structures in 4 dimensions0 57K45Higher-dimensional knots and links0 57K50Low-dimensional manifolds of specific dimension 5 or higher0 57K99Low-dimensional topology in specific dimensions0

Mapped problems

OP-10090Geometry and topologyStatus unassessed

Torsion and the torsion-free quotient of homology cobordism

A question from Bulletin of the American Mathematical Society (2024). Problem O; inspected PDF p. 13.

Oğuz Şavk — A survey of the homology cobordism group· Journal question · editorial summary

OP-10089Geometry and topologyStatus unassessed

The three fibers question for homology balls

A question from Bulletin of the American Mathematical Society (2024). Problem G (Three Fibers Conjecture); inspected PDF p. 9.

Oğuz Şavk — A survey of the homology cobordism group· Journal question · editorial summary

OP-10088Geometry and topologyStatus unassessed

Seifert spheres bounding homology balls but no contractible manifold

A question from Bulletin of the American Mathematical Society (2024). Problem F; inspected PDF p. 9.

Oğuz Şavk — A survey of the homology cobordism group· Journal question · editorial summary

OP-10087Geometry and topologyStatus unassessed

Is the integral homology cobordism group free abelian?

A question from Bulletin of the American Mathematical Society (2024). Problem A; inspected PDF p. 5.

Oğuz Şavk — A survey of the homology cobordism group· Journal question · editorial summary

OP-12028Geometry and topologyOpen

Tight alternating knot constant ( $C_{22b}$ )

Tight alternating knot constant: determine C 22b or improve its bounds; the repository records 0.017 (lower) and 7.31 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12027Geometry and topologyOpen

Tight knot constant ( $C_{22a}$ )

Tight knot constant: determine C 22a or improve its bounds; the repository records 1.105 (lower) and 10.76 (10.02 ) (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-11985Geometry and topologyOpen

The Smooth Four-Dimensional Poincaré Conjecture

The Smooth Four-Dimensional Poincaré Conjecture. Breakthrough problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11983Geometry and topologyOpen

The Slice–Ribbon Conjecture and the GST Knot

The Slice–Ribbon Conjecture and the GST Knot. Solid result problem from Epoch AI’s FrontierMath: Open Problems; answers are checked by a verifier program.

Epoch AI — FrontierMath: Open Problems· Licensed source statement· 2026

OP-11965Geometry and topologyOpen