A sheaf homology theory with supports

Jacobs, Philippe

Illinois J. Math., Tome 44 (2000) no. 4, p. 644-666 / Harvested from Project Euclid

Résumé

We introduce a homology theory with supports and with coefficients in a sheaf. It has a very explicit description of the chains in terms of a triangulation of an ambient space, making the theory useful for integration purposes. We prove a Poincaré Duality Theorem that states that our homology modules are isomorphic to the classical sheaf cohomology modules with supports. This theorem is a main ingredient in the proof of a criterion on the vanishing of real principal value integrals in terms of cohomology. We briefly explain how real principal value integrals appear as residues of poles of distributions $|f|^{s}$ and as coefficients of asymptotic expansions of oscillating integrals.

Publié le : 2000-09-15
Classification: 11S40, 14F99, 55N30, 55N35, 57R19

@article{1256060422,
     author = {Jacobs, Philippe},
     title = {A sheaf homology theory with supports},
     journal = {Illinois J. Math.},
     volume = {44},
     number = {4},
     year = {2000},
     pages = { 644-666},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1256060422}
}

Jacobs, Philippe. A sheaf homology theory with supports. Illinois J. Math., Tome 44 (2000) no. 4, pp.  644-666. http://gdmltest.u-ga.fr/item/1256060422/