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A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A short mnemonic for remembering the first seven decimal digits of pi is "How I wish I could calculate pi" (C. Heckman, pers. comm., Feb. 3, 2005). Eight digits are given by ...

The Skewes number (or first Skewes number) is the number Sk_1 above which pi(n)<li(n) must fail (assuming that the Riemann hypothesis is true), where pi(n) is the prime ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

A subset E of a topological space S is said to be meager if E is of first category in S, i.e., if E can be written as the countable union of subsets which are nowhere dense ...

The Dehn invariant is a constant defined using the angles and edge lengths of a three-dimensional polyhedron. It is significant because it remains constant under polyhedron ...

The universal cover of a connected topological space X is a simply connected space Y with a map f:Y->X that is a covering map. If X is simply connected, i.e., has a trivial ...

Given a compact manifold M and a transversely orientable codimension-one foliation F on M which is tangent to partialM, the pair (M,F) is called a generalized Reeb component ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...