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http://dx.doi.org/10.4134/CKMS.c170463

MAYER-VIETORIS SEQUENCE IN COHOMOLOGY OF LIE ALGEBROIDS ON SIMPLICIAL COMPLEXES  

Oliveira, Jose R. (Department of Mathematics Minho University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.4, 2018 , pp. 1357-1366 More about this Journal
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.
Keywords
Lie algebroid cohomology; Mayer-Vietoris sequence; simplicial space; piecewise smooth forms;
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  • Reference
1 D. Sullivan, Differential forms and the topology of manifolds, in Manifolds-Tokyo 1973 (Proc. Internat. Conf., Tokyo, 1973), 37-49, Univ. Tokyo Press, Tokyo, 1975.
2 D. Sullivan, Infinitesimal computations in topology, Publ. Math. Inst. Hautes Etudes Sci. 47 (1977), 269-331.   DOI
3 H. Whitney, Geometric Integration Theory, Princeton University Press, Princeton, NJ, 1957.
4 J. A. Alvarez Lopez and M. Calaza, Witten's perturbation on strata, Asian J. Math. 21 (2017), no. 1, 47-125.   DOI
5 P. A. Griffiths and J. W. Morgan, Rational Homotopy Theory and Differential Forms, Progress in Mathematics, 16, Birkhauser, Boston, MA, 1981.
6 R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, 82, Springer-Verlag, New York, 1982.
7 M. Crainic and R. L. Fernandes, Integrability of Lie brackets, Ann. of Math. (2) 157 (2003), no. 2, 575-620.   DOI
8 S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton University Press, Princeton, New Jersey, 1952.
9 J. Kubarski, Poincare duality for transitive unimodular invariantly oriented Lie algebroids, Topology Appl. 121 (2002), no. 3, 333-355.   DOI
10 K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Mathematical Society Lecture Note Series, 213, Cambridge University Press, Cambridge, .
11 A. S. Mishchenko and J. R. Oliveira, Sullivan-Whitney constructions for transitive Lie algebroids, to appear.
12 S. Li and A. S. Mishchenko, Classification of Couplings for Transitive Lie Algebroids, Dokl. Math. 91 (2015), no. 1, 84-86; translated from Dokl. Akad. Nauk 460 (2015), no. 5, 517-519.   DOI
13 X. Li and A. S. Mishchenko, The existence and classification of couplings between Lie algebra bundles and tangent bundles, Topology Appl. 201 (2016), 291-308.   DOI