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| On a Spectral Sequence for Twisted Cohomologies |
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Citation： |
Weiping LI,Xiugui LIU,He WANG.On a Spectral Sequence for Twisted Cohomologies[J].Chinese Annals of Mathematics B,2014,35(4):633~658 |
| Page view： 1443
Net amount： 875 |
Authors： |
Weiping LI; Xiugui LIU; He WANG; |
Foundation： |
the National Natural Science Foundation of China (No. 11171161) and
the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education
Ministry (No. 2012940). |
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| Abstract： |
Let ($\Omega^{\ast}(M), d$) be the de Rham cochain complex for a
smooth compact closed manifolds $M$ of dimension $n$. For an
odd-degree closed form $H$, there is a twisted de Rham cochain
complex $(\Omega^{\ast}(M), d+H_\wedge)$ and its associated twisted
de Rham cohomology $H^*(M,H)$. The authors show that there exists a
spectral sequence $\{E^{p, q}_r, d_r\}$ derived from the filtration
$F_p(\Omega^{\ast}(M))=\bigoplus\limits_{i\geq p}\Omega^i(M)$ of
$\Omega^{\ast}(M)$, which converges to the twisted de Rham
cohomology $H^*(M,H)$. It is also shown that the differentials in
the spectral sequence can be given in terms of cup products and
specific elements of Massey products as well, which generalizes a
result of Atiyah and Segal. Some results about the indeterminacy of
differentials are also given in this paper. |
Keywords： |
Spectral sequence, Twisted de Rham cohomology, Massey product,
Differential |
Classification： |
58J52, 55T99, 81T30 |
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