301 problems

Ganea's conjecture is a now disproved claim in algebraic topology. It states that

In mathematics, Nikiel's conjecture in general topology was a conjectural characterization of the continuous image of a compact total order. The conjecture was first formulated by…

In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with i…

In the mathematical field of geometric topology, the Poincaré conjecture is a theorem about the characterization of the 3-sphere.

In geometric topology, the spherical space form conjecture states that a finite group acting on the 3-sphere is conjugate to a group of isometries of the 3-sphere.

In mathematics, the cobordism hypothesis, due to John C. Baez and James Dolan, concerns the classification of extended topological quantum field theories (TQFTs). In 2008, Jacob Lu…

In mathematics, the Atiyah conjecture is a collective term for a number of statements about restrictions on possible values of -Betti numbers.

In mathematics, the Ehrenpreis conjecture of Leon Ehrenpreis states that for any K greater than 1, any two closed Riemann surfaces of genus at least 2 have finite-degree covers whi…

In differential geometry, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S3. The conjecture was featured by the Australian…

In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is…

In mathematics, more specifically symplectic topology, the nearby Lagrangian conjecture, is an open mathematical problem often attributed to Vladimir Arnold. It states that every c…

In mathematics, the Zeeman conjecture or Zeeman's collapsibility conjecture asks whether given a finite contractible 2-dimensional CW complex $K$, the space $K\times [0,1]$ is coll…

The Whitehead conjecture is a claim in algebraic topology. It was formulated by J. H. C. Whitehead in 1941. It states that every connected subcomplex of a two-dimensional aspherica…

In the branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of their complements.

In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types…

In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 198…

The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965.

In mathematics, the Hilbert–Smith conjecture is concerned with the transformation groups of manifolds; and in particular with the limitations on topological groups G that can act e…

In rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician Stephen Halperin.

In geometric topology, the Borel conjecture asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, ass…

In mathematics, the Bing–Borsuk conjecture states that every -dimensional homogeneous absolute neighborhood retract space is a topological manifold. The conjecture has been proved…

In the mathematical theory of knots, a Berge knot or doubly primitive knot is any member of a particular family of knots in the 3-sphere. A Berge knot K is defined by the condition…

In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the reduced C-algebra of a group and the K-homology of the cla…

Let $M$ be a compact manifold. The analytic torsion is the invariant defined from the zeta-regularized determinants of the Laplacians on differential forms, while the R-torsion is…

Chern's conjecture. The Euler characteristic of $M$ is zero.