Symmetric product
Encyclopedia
In mathematics, the term symmetric product can refer to:
- The symmetric part of a tensor
- The symmetric product of an algebraic curveSymmetric product of an algebraic curveIn mathematics, the n-fold symmetric product of an algebraic curve C is the quotient space of the n-fold cartesian productor Cn by the group action of the symmetric group on n letters permuting the factors. It exists as a smooth algebraic variety ΣnC; if C is a compact Riemann surface it is...
- The infinite symmetric productInfinite symmetric productIn algebraic topology, the infinite symmetric product SP of a topological space X with given basepoint e is the quotient of the disjoint union of all powers X, X2, X3, .....
SP(X) of a space X in algebraic topology