The authors introduce a kind of slowly increasing cohomology HS＊（X） for a discrete metric space X with polynomial growth, and construct a character map from the slowly increasing cohomology HS＊ （X） into HC＊ont ...The authors introduce a kind of slowly increasing cohomology HS＊（X） for a discrete metric space X with polynomial growth, and construct a character map from the slowly increasing cohomology HS＊ （X） into HC＊ont （S（X））, the continuous cyclic cohomol- ogy of the smooth subalgebra S（X） of the uniform Roe algebra B＊ （X）. As an application, it is shown that the fundamental cocycle, associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth, is slowly increasing.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11171245)the Major Program of National Natural Science Foundation of China(No.10731020)the Shanghai Municipal Natural Science Foundation(No.09ZR1402000)
文摘The authors introduce a kind of slowly increasing cohomology HS＊（X） for a discrete metric space X with polynomial growth, and construct a character map from the slowly increasing cohomology HS＊ （X） into HC＊ont （S（X））, the continuous cyclic cohomol- ogy of the smooth subalgebra S（X） of the uniform Roe algebra B＊ （X）. As an application, it is shown that the fundamental cocycle, associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth, is slowly increasing.
