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The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism.

The study of map projections and the making of geographical maps.

A diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

A map which is monotone increasing and therefore order-preserving.

A nonsingular linear map A:R^n->R^n is orientation-preserving if det(A)>0.

A nonsingular linear map A:R^n->R^n is orientation-reversing if det(A)<0.

A line segment joining the midpoints of opposite sides of a quadrilateral or tetrahedron. Varignon's theorem states that the bimedians of a quadrilateral bisect each other ...

Relates invariants of a curve defined over the integers. If this inequality were proven true, then Fermat's last theorem would follow for sufficiently large exponents. ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...