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An upper bound on the sum of the Betti numbers of real varieties though Morse theory

Riccardo Caniato
Institution: 
SISSA
Location: 
A-133
Schedule: 
Thursday, June 27, 2019 - 14:30
Abstract: 

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. 

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