Formal barycenter spaces with weights: the Euler characteristic

Sadok Kallel



We compute the Euler characteristic with compact supports $\chi_c$ of the formal barycenter spaces with weights of some locally compact spaces, connected or not. This reduces to the topological Euler characteristic $\chi$ when the weights of the singular points are less than one. As foresighted by Andrea Malchiodi, our formula is related to the Leray-Schauder degree for mean field equations on a compact Riemann surface obtained by C.C. Chen and C.S.\ Lin.


Euler characteristic; compact supports; Leray-Schauder degree; stratification

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