Doman Takata

Geometric $K$-homology and operator $K$-theory for Hilbert manifolds

Poincar\'e duality is a classical theorem relating the homology and cohomology of closed oriented manifolds. This theorem has been extended to more general settings and to generalized (co)homology theories, including $K$-theory. In this paper, we construct an infinite-dimensional analogue of the $K$-theoretic Poincar\'...