Dold–Thom theorem

In algebraic topology, the Dold–Thom theorem, proved by Albrecht Dold and Thom (1956, 1958), states that the homotopy group π_i(SP(X)) of the infinite symmetric product SP(X) of X is the i-th singular reduced homology group of "X", usually denoted by H_i(X,Z) with an added ~ (tilde) on the H.

References

• Dold, Albrecht; Thom, René (1956), "Une généralisation de la notion d'espace fibré. Application aux produits symétriques infinis", Les Comptes rendus de l'Académie des sciences 242: 1680–1682, MR0077121 
• Dold, Albrecht; Thom, René (1958), "Quasifaserungen und unendliche symmetrische Produkte", Annals of Mathematics. Second Series 67: 239–281, ISSN 0003-486X, JSTOR 1970005, MR0097062