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| On Cohomology of Infinitesimal Neighbourhoods of Complex Manifolds |
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Citation： |
Xiao Erjian.On Cohomology of Infinitesimal Neighbourhoods of Complex Manifolds[J].Chinese Annals of Mathematics B,1985,6(3):351~358 |
| Page view： 762
Net amount： 831 |
Authors： |
Xiao Erjian; |
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| Abstract： |
In this paper, we introduce the concept of the (k, l)-th C^\infinity infinitesimal neighbourhoods of complex manifold M and difine defferential modules $mathscr{A}^{p,q}_{M,k-p,l-q}$ and $mathscr{A}^\tau_{M,k,l}$ for
the (k, l)-th C^\infinity infinitesimal neighbourhoods. We prove some isomorphism theorems of cohomology and hyper cohomology concerning $[\tilde \Omega]^p_{M,k-q}$and $\Omega^p_{M,k-p}$ as follows
$H^p(M,[\tilde \Omega]^\tau_{M,k-r})\approxH^p-\varepsilon(M,[\tilde mathscr{A}]^\tau_{M,k-r,l-*}),$
$H^p(M,[\tilde mathscr{A}]^*_{M,k,l})\approxH^p_D^R(M,C)$
and for hyper cohomology
$H^p(M,[\tilde \Omega]^*_{M,k-*})\approxH^p(M,C),$
$H^p(M,\Omega^*_{M,k-*}\approxH^p(M,C_M).$ |
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