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| Slowly Increasing Cohomology for Discrete Metric Spaces with Polynomial Growth |
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Citation： |
Xiaoman CHEN,Shuyun WEI.Slowly Increasing Cohomology for Discrete Metric Spaces with Polynomial Growth[J].Chinese Annals of Mathematics B,2012,33(5):681~694 |
| Page view： 1805
Net amount： 1226 |
Authors： |
Xiaoman CHEN; Shuyun WEI; |
Foundation： |
the National Natural Science Foundation of China (No. 11171245), the Major Program of National Natural Science Foundation of China (No. 10731020) and the Shanghai Municipal Natural Science Foundation (No. 09ZR1402000). |
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| Abstract： |
The authors introduce a kind of slowly increasing cohomology ${\rm HS}^*(X)$ for a discrete metric space $X$ with polynomial growth, and construct a character map from the slowly increasing cohomology ${\rm HS}^*(X)$ into ${\rm HC}_{\rm cont}^*(S(X))$, the continuous cyclic cohomology 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. |
Keywords： |
Slowly increasing cohomology, Polynomial growth, Uniform Roe algebra |
Classification： |
46L80 |
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