Stability of the Rational Homotopy Type of Moduli Spaces
Abstract
We show that for g > 2k+2 the k-rational homotopy type of the moduli space Mg,n of algebraic curves of genus g with n punctures is independent of g, and the space Mg,n is k-formal. This implies the existence of a limiting rational homotopy type of Mg,n as g goes to infinity and the formality of it.
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