A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces

Details A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces

2006-02-06

arxiv.org/abs/math/0602111v3

Journal of the European Mathematical Society, vol.10 (1) 2008, pp.231-241

Mathematics

Algebraic Geometry

LaTex, 12 pages, final version

Scientific paper

Inspired by his vanishing results of tautological classes and by Harer's computation of the virtual cohomological dimension of the mapping class group, Looijenga conjectured that the moduli space of smooth Riemann surfaces admits a stratification by affine subsets with a certain number of layers. Similarly, Roth and Vakil extended the conjecture to the moduli spaces of Riemann surfaces of compact type, of Riemann surfaces with rational tails and of Riemann surfaces with at most k rational components. As a consequence of Lefschetz's theorem, Roth-Vakil's conjecture would also imply that the previous (coarse) moduli spaces are homotopy equivalent to cellular complexes of a certain dimension. Using Harer's computation for the moduli spaces of smooth Riemann surfaces, we prove this last statement.

Affiliated with

Also associated with

No associations

Rating

A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A remark on the virtual homotopical dimension of some moduli spaces of stable Riemann surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-63380