$Z^2$

$Z$

$S^1$

$Z imes Z$

A theorem relating the homology and cohomology of a manifold.

A theorem relating the fundamental group and the homology of a manifold.

A theorem relating the Euler characteristic and the genus of a surface.

A theorem relating the curvature and the topology of a manifold.

A closed curve in 3-space.

A closed surface in 3-space.

A closed 3-manifold.

A closed 4-manifold.

A polynomial that is associated to a knot and is an invariant of the knot.

A polynomial that is associated to a knot and is not an invariant of the knot.

A polynomial that is associated to a knot and is not an invariant of the knot.

A polynomial that is associated to a knot and is not an invariant of the knot.

A conjecture that states that every 3-manifold can be decomposed into a collection of simpler pieces.

A conjecture that states that every 3-manifold can be decomposed into a collection of simpler pieces.

A conjecture that states that every 3-manifold can be decomposed into a collection of simpler pieces.

A conjecture that states that every 3-manifold can be decomposed into a collection of simpler pieces.

A theorem that states that every 3-manifold can be obtained by performing Dehn surgery on a link in a 3-sphere.

A theorem that states that every 3-manifold can be obtained by performing Dehn surgery on a link in a 3-sphere.

A theorem that states that every 3-manifold can be obtained by performing Dehn surgery on a link in a 3-sphere.

A theorem that states that every 3-manifold can be obtained by performing Dehn surgery on a link in a 3-sphere.

An invariant of a 3-manifold that is defined using Heegaard splittings.

An invariant of a 3-manifold that is defined using Heegaard splittings.

An invariant of a 3-manifold that is defined using Heegaard splittings.

An invariant of a 3-manifold that is defined using Heegaard splittings.

A homology theory for 3-manifolds that is defined using Morse theory.

A homology theory for 3-manifolds that is defined using Morse theory.

A homology theory for 3-manifolds that is defined using Morse theory.

A homology theory for 3-manifolds that is defined using Morse theory.

An invariant of a 4-manifold that is defined using gauge theory.

An invariant of a 4-manifold that is defined using gauge theory.

An invariant of a 4-manifold that is defined using gauge theory.

An invariant of a 4-manifold that is defined using gauge theory.

An invariant of a 4-manifold that is defined using Donaldson theory.

An invariant of a 4-manifold that is defined using Donaldson theory.

An invariant of a 4-manifold that is defined using Donaldson theory.

An invariant of a 4-manifold that is defined using Donaldson theory.

An invariant of a symplectic 4-manifold that is defined using Gromov-Witten theory.

An invariant of a symplectic 4-manifold that is defined using Gromov-Witten theory.

An invariant of a symplectic 4-manifold that is defined using Gromov-Witten theory.

An invariant of a symplectic 4-manifold that is defined using Gromov-Witten theory.

A homology theory for links that is defined using categorification.

A homology theory for links that is defined using categorification.

A homology theory for links that is defined using categorification.

A homology theory for links that is defined using categorification.

An invariant of a knot that is defined using Khovanov homology.

An invariant of a knot that is defined using Khovanov homology.

An invariant of a knot that is defined using Khovanov homology.

An invariant of a knot that is defined using Khovanov homology.

A homology theory for 3-manifolds that is defined using Heegaard splittings and Floer theory.

A homology theory for 3-manifolds that is defined using Heegaard splittings and Floer theory.

A homology theory for 3-manifolds that is defined using Heegaard splittings and Floer theory.

A homology theory for 3-manifolds that is defined using Heegaard splittings and Floer theory.