analytic manifold
topological manifold with analytic transition maps
Lie group
group that is also a smooth manifold with group operations that are smooth
knot complement
complement of a knot in three-sphere
cylinder
surface formed by the points at a fixed distance from a given straight line called the axis of the cylinder; one of the most basic curvilinear geometric shapes
Euclidean space
generalization of Euclidean geometry to higher-dimensional vector spaces
complex manifold
manifold with an atlas of charts to the open unit disk in ℂⁿ, such that the transition maps are holomorphic
circle
simple curve of Euclidean geometry
helix
smooth space curve
real projective space
type of topological space
sphere
round, rotationally symmetric shape of the 2D surface of a ball in 3D space