Mathematics

The aim of the talk is to show that the sum of the Betti numbers of a real affine algebraic variety in the n-dimensional real affine space is bounded above by a constant depending only on the maximum degree of the polynomials defining the locus and from the dimension of the ambient space n; first, the particular case of a compact and regular hypersurface is studied through Morse theory and then, by means of semi-algebraic triviality theorems, the statement is extended to drop the compactness and regularity hypotheses.