Israel Journal of Mathematics

, Volume 90, Issue 1, pp 93–113

On graded quotient modules of mapping class groups of surfaces

Article

DOI: 10.1007/BF02783208

Cite this article as:
Asada, M. & Nakamura, H. Israel J. Math. (1995) 90: 93. doi:10.1007/BF02783208

Abstract

Let Γg, n be the mapping class group of a compact Riemann surface of genusg withn points preserved (2−2gn<0,g≥1,n≥0). The Torelli subgroup of Γg, n has a natural weight filtration {Γg, n(m)}m≥1. Each graded quotient grmΓg, n ⊗ ℚ (m≥1) is a finite dimensional vector space over ℚ on which the group Sp(2g, ℚ)×Sn naturally acts.

In this paper, we have determined the Sp(2g, ℚ)×Sn module structure of grm Γg, n ⊗ ℚ for 1≤m≤3. This includes a verification of an expectation by S. Morita. Also, for generalm, we have identified a certain Sp(2g, ℚ)-irreducible component of grm Γg, n ⊗ ℚ by constructing explicitly elements in these modules.

Copyright information

© Hebrew University 1995

Authors and Affiliations

  1. 1.Faculty of EngineeringTokyo Denki UniversityTokyoJapan
  2. 2.Department of Mathematical SciencesUniversity of TokyoHongo, TokyoJapan

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