Dold–Thom theorem

In algebraic topology, the Dold–Thom theorem, proved by Albrecht Dold and René Thom (1956, 1958), states that the homotopy group π_i(SP(X)) of the infinite symmetric product SP(X) of a connected CW complex X is the i-th singular reduced homology group of X, usually denoted by ${\displaystyle {\widetilde {H}}_{i}(X;\mathbb {Z} )}$.^[1] Almgren Isomorphism Theorem is a generalization of the Dold-Thom theorem.

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, MR 0077121
• Dold, Albrecht; Thom, René (1958), "Quasifaserungen und unendliche symmetrische Produkte", Annals of Mathematics, Second Series, 67 (2): 239–281, doi:10.2307/1970005, ISSN 0003-486X, JSTOR 1970005, MR 0097062

Specific

External links[]

• The Dold-Thom theorem for infinity categories?

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