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- W1479996312 abstract "We study the cohomology $H^*_{lambda omega}(G/Gamma, {mathbb C})$ of the deRham complex $Lambda^*(G/Gamma)otimes{mathbb C}$ of a compact solvmanifold $G/Gamma$ with a deformed differential $d_{lambda omega}=d + lambdaomega$, where $omega$ is a closed 1-form. This cohomology naturally arises in the Morse-Novikov theory. We show that for a solvable Lie group $G$ with a completely solvable Lie algebra $mathfrak{g}$ and a cocompact lattice $Gamma subset G$ the cohomology $H^*_{lambda omega}(G/Gamma, {mathbb C})$ coincides with the cohomology $H^*_{lambda omega}(mathfrak{g})$ of the Lie algebra $mathfrak{g}$ associated with the one-dimensional representation $rho_{lambda omega}: mathfrak{g} to {mathbb K}, rho_{lambda omega}(xi) = lambda omega(xi)$. Moreover $H^*_{lambda omega}(G/Gamma, {mathbb C})$ is non-trivial if and only if $-lambda [omega]$ belongs to the finite subset ${0} cup tilde Omega_{mathfrak{g}}$ in $H^1(G/Gamma, {mathbb C})$ well defined in terms of $mathfrak{g}$." @default.
- W1479996312 created "2016-06-24" @default.
- W1479996312 creator A5087337281 @default.
- W1479996312 date "2002-03-07" @default.
- W1479996312 modified "2023-09-27" @default.
- W1479996312 title "Cohomology with local coefficients of solvmanifolds and Morse-Novikov theory" @default.
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