Stability of the Rational Homotopy Type of Moduli Spaces

Details Stability of the Rational Homotopy Type of Moduli Spaces Stability of the Rational Homotopy Type of Moduli Spaces

1997-08-22

arxiv.org/abs/alg-geom/9708019v1

Mathematics

Algebraic Geometry

7 pages, 1 figure

Scientific paper

We show that for g > 2k+2 the k-rational homotopy type of the moduli space
M_{g,n} of algebraic curves of genus g with n punctures is independent of g,
and the space M_{g,n} is k-formal. This implies the existence of a limiting
rational homotopy type of M_{g,n} as g goes to infinity and the formality of
it.

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