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A principal bundle is a special case of a fiber bundle where the fiber is a group G. More specifically, G is usually a Lie group. A principal bundle is a total space E along ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

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 ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

There are two definitions of the supersingular primes: one group-theoretic, and the other number-theoretic. Group-theoretically, let Gamma_0(N) be the modular group Gamma0, ...

A Kähler structure on a complex manifold M combines a Riemannian metric on the underlying real manifold with the complex structure. Such a structure brings together geometry ...

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

An ANOVA in which the number of replicates (sets of identical observations) is restricted to be the same for each factor level (treatment group).

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.