Abstract
For the cohomology of a sheaf of Abelian groups with involution on a topological space, inequalities that are analogs of the classical Harnack--Thom inequality for the cohomology of a topological space with involution are proved. The general inequalities obtained are applied to reprove some known inequalities and prove new ones.
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REFERENCES
V. A. Krasnov, “The Harnack–Thom inequalities for maps of real algebraic varieties, ” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 47 (1983), no. 2, 268–297.
A. Grothendieck, Sur quelques points d'algèbre homologique, Japan, 1957.
V. A. Krasnov, “Degenerations of real algebraic varieties, ” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 49 (1985), no. 4, 798–837.
V. A. Krasnov, “The Harnack–Thom inequality for a critical point of a polynomial, ” Mat. Zametki [Math. Notes], 38 (1985), no. 5, 717–720.
J. Milnor, Singular Points of Complex Hypersurfaces, Princeton Univ. Press, Princeton, NJ, 1968.
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Krasnov, V.A. The Harnack--Thom Inequalities for Sheaves with Involution and Their Applications. Mathematical Notes 74, 647–655 (2003). https://doi.org/10.1023/B:MATN.0000008997.25584.0a
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DOI: https://doi.org/10.1023/B:MATN.0000008997.25584.0a