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- W2759836723 abstract "Let $M$ be a smooth manifold, smoothly triangulated by a simplicial complex $K$, and $cA$ a transitive Lie algebroid on $M$. The Lie algebroid restriction of $cA$ to a simplex $Delta$ of $K$ is denoted by $cA^{!!}_{Delta}$. A piecewise smooth form of degree $p$ on $cA$ is a family $omega=(omega_{Delta})_{Deltain K}$ such that $omega_{Delta}in Omega^{p}(cA^{!!}_{Delta};Delta)$ for each $Deltain K$, satisfying the compatibility condition concerning the restrictions of $omega_{Delta}$ to the faces of $Delta$, that is, if $Delta'$ is a face of $Delta$, the restriction of the form $omega_{Delta}$ to the simplex $Delta'$ coincides with the form $omega_{Delta'}$. The set $Omega^{ast}(cA;K)$ of all piecewise smooth forms on $cA$ is a cochain algebra. One has a natural morphism $$Omega^{ast}(cA;M)rightarrow Omega^{ast}(cA;K)$$ of cochain algebras given by restriction of a smooth form defined on $cA$ to a smooth form defined on $cA^{!!}_{Delta}$, for all simplices $Delta$ of $K$. In this paper, we prove that, for triangulated compact manifolds, the cohomology of this construction is isomorphic to the Lie algebroid cohomology of $cA$, in which the isomorphism is induced by the restriction map." @default.
- W2759836723 created "2017-10-06" @default.
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- W2759836723 date "2017-09-21" @default.
- W2759836723 modified "2023-09-26" @default.
- W2759836723 title "Sullivan constructions for transitive Lie algebroids - smooth case" @default.
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