Homology of Lie groups and Poincaré duality (Q799276)

Let G be a Lie group with a finite number of components. The authors define and study the differential homology groups \(H_ i(G,A)\) with the coefficients in the differentiable G-module A. They also prove the Poincaré type theorem: \(H_ i(G,A)\simeq H^{n-i}(G,A\otimes {\mathbb{R}}_{\delta}),\) here \(n=\dim G/K\) (K being the maximal compact subgroup of G), \(\delta\) the modular function of G.