Mayer-Vietoris sequence in cohomology of Lie algebroids on simplicial complexes
Jose R. Oliveira
TL;DR
This paper demonstrates that the Mayer-Vietoris sequence applies to the cohomology of Lie algebroids on simplicial complexes, under certain compatibility conditions, extending the theoretical framework of Lie algebroid cohomology.
Contribution
It establishes the validity of the Mayer-Vietoris sequence for Lie algebroids on simplicial complexes, using an extension lemma for piecewise smooth forms.
Findings
Mayer-Vietoris sequence holds for Lie algebroid cohomology on simplicial complexes.
Extension lemma for piecewise smooth forms is key to the proof.
Compatibility conditions ensure the sequence's applicability.
Abstract
It is shown that the Mayer-Vietoris sequence holds for the cohomology of complexes of Lie algebroids which are defined on simplicial complexes and satisfy the compatibility condition concerning restrictions to the faces of each simplex. The Mayer-Vietoris sequence will be obtained as a consequence of the extension lemma for piecewise smooth forms defined on complexes of Lie algebroids.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models