I want to know if there IS a notion of DUALITY between the homotopy and homology of groups, namely topological manifolds given group structure. i.e, is there an equivalence between the number of simple closed curves or 'paths' that generate the space, and the number of connected components that generate the same given space. I am reading Differential Forms in Algebraic Topology by Bott and Tuu, if anyone has insight into the book. I am fairly strong in my topology but not as strong in my algebra. THANKS!
2026-03-29 09:11:48.1774775508
duality between homotopy and homology of manifolds
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