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The real projective plane with elliptic metric where the distance between two points P and Q is defined as the radian angle between the projection of the points on the ...

If f:E->B is a fiber bundle with B a paracompact topological space, then f satisfies the homotopy lifting property with respect to all topological spaces. In other words, if ...

A set in R^d formed by translating an affine subspace or by the intersection of a set of hyperplanes.

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

f(I) is the collection of all real-valued continuous functions defined on some interval I. f^((n))(I) is the collection of all functions in f(I) with continuous nth ...

A non-Euclidean space with constant negative Gaussian curvature.

A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

A knot move illustrated above. Two knots cannot be distinguished using Vassiliev invariants of order <=n iff they are related by a sequence of such moves (Habiro 2000). There ...

A handlebody of type (n,k) is an n-dimensional manifold that is attained from the standard n-disk by attaching only k-D handles.

A diagram expressing how the gluing operation that connects the handlebodies involved in a Heegaard splitting proceeds, usually by showing how the meridians of the handlebody ...