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Titolo: On topological and homotopy invariant combinations of Hodge and Chern numbers

Abstract: In 1954 Hirzebruch asked which linear combinations of Hodge and Chern numbers are topological invariant of Kähler manifolds. In this contest we can reinterpret the word “topological” to consider both homeomorphic and diffeomorphic invariants. Sixty years later Kotschick and Schreieder solved this problem. They showed that there are no unexpected linear combinations of Hodge and Chern numbers which are topologically invariant. Their main idea was to introduce the Hodge ring of Kähler manifolds. This ring keeps track of Hodge numbers in the same way the classical complex cobordism ring keeps track of Chern numbers. I will explain how these objects allowed them to achieve a solution. Moreover, I will present a slight modification of the original problem, asking which linear combinations of Hodge and Chern numbers of Kähler manifolds are preserved by homotopy equivalences. We will focus on a possible approach and on the difficulties that one encounters in this case.

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https://web.unica.it/unica/it/gruppo_geo_differenziale.page