Simplicial volume of moduli spaces of riemann surfaces

Lizhen Ji University of Michigan

Differential Geometry mathscidoc:1609.10259

Journal of Differential Geometry, 90, (3), 413-437, 2012
Motivated by results on the simplicial volume of locally symmetric spaces of finite volume, in this note, we observe that the simplicial volume of the moduli space Mg,n is equal to 0 if g  2; g = 1, n  3; or g = 0, n  6; and the orbifold simplicial volume of Mg,n is positive if g = 1, n = 0, 1; g = 0, n = 4. We also observe that the simplicial volume of the Deligne-Mumford compactification of Mg,n is equal to 0, and the simplicial volumes of the reductive Borel-Serre compactification of arithmetic locally symmetric spaces ..\X and the Baily-Borel compactification of Hermitian arithmetic locally symmetric spaces ..\X are also equal to 0 if the Q-rank of ..\X is at least 3 or if ..\X is irreducible and of Q-rank 2.
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@inproceedings{lizhen2012simplicial,
  title={SIMPLICIAL VOLUME OF MODULI SPACES OF RIEMANN SURFACES},
  author={Lizhen Ji},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224614824813921},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={3},
  pages={413-437},
  year={2012},
}
Lizhen Ji. SIMPLICIAL VOLUME OF MODULI SPACES OF RIEMANN SURFACES. 2012. Vol. 90. In Journal of Differential Geometry. pp.413-437. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913224614824813921.
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