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A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

A group of sociable numbers of order 3.

A finite set of contraction maps w_i for i=1, 2, ..., N, each with a contractivity factor s<1, which map a compact metric space onto itself. It is the basis for fractal image ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

Sigma is the eighteenth letter of the ancient Greek alphabet. As an upper case letter (Sigma), it is used as a symbol for sums and series. As a lower case letter (sigma) it ...

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

The geometry of the Lie group consisting of real matrices of the form [1 x y; 0 1 z; 0 0 1], i.e., the Heisenberg group.

The set of elements g of a group such that g^(-1)Hg=H, is said to be the normalizer N_G(H) with respect to a subset of group elements H. If H is a subgroup of G, N_G(H) is ...

The intersection phi(G) of all maximal subgroups of a given group G.