Non-trivial 1-classes in the homology of the real moduli spaces M-bar_{0,n} and related structures

We give lower bounds for the rank of the first homology group of the real points of the Deligne-Mumford-Knudsen compactification of stable n-pointed curves of genus 0,which coincides with the Chow quotient (RP^1)^n//PGL(2,R).The study has connections with spectral geometry and combinatorics.