The Harnack–Thom Inequalities for Sheaves with Involution and Their Applications

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.