An equivariant Poincaré duality for proper cocompact actions by matrix groups

[摘要] Let GGG be a linear Lie group acting properly on a GGG-spinc\mathrm{spin}^cspinc manifold MMM with compact quotient. We give a short proof that Poincaré duality holds between GGG-equivariant KKK-theory of MMM, defined using finite-dimensional GGG-vector bundles, and GGG-equivariant KKK-homology of MMM, defined through the geometric model of Baum and Douglas.

[学科分类] 神经科学

[关键词] Poincaré duality;equivariant;matrix groups;linear groups