241203 Olivier de Gaay Fortman

Let X be a nice topological space equipped with an involution s, and let X^s be the space of fixed points. A classical result says that, for cohomology with Z/2-coefficients, the dimension of the cohomology ring of X^s is bounded from above by the dimension of the cohomology ring of X. This inequality is called the Smith—Thom inequality. The goal of this talk is to conjecture a natural generalization of this inequality for topological stacks (and in particular, for orbifolds) equipped with an involution, and prove this in various cases. This has applications for the study of moduli spaces in real algebraic geometry. This is joint work with Emiliano Ambrosi.