ABELIAN COVERS OF SURFACES AND THE HOMOLOGY OF THE LEVEL L MAPPING CLASS GROUP-Reference-Cited by-同舟云学术

ABELIAN COVERS OF SURFACES AND THE HOMOLOGY OF THE LEVEL L MAPPING CLASS GROUP

Published:2011-09 Issue:03 Volume:03 Page:265-306
ISSN:1793-5253
Container-title:Journal of Topology and Analysis
language:en
Short-container-title:J. Topol. Anal.

Author:

PUTMAN ANDREW¹

Affiliation:

1. Department of Mathematics, Rice University, MS 136, 6100 Main St., Houston, TX 77005, USA

Abstract

We calculate the first homology group of the mapping class group with coefficients in the first rational homology group of the universal abelian ℤ/L-cover of the surface. If the surface has one marked point, then the answer is ℚτ(L), where τ(L) is the number of positive divisors of L. If the surface instead has one boundary component, then the answer is ℚ. We also perform the same calculation for the level L subgroup of the mapping class group. Set HL = H1(Σg; ℤ/L). If the surface has one marked point, then the answer is ℚ[HL], the rational group ring of HL. If the surface instead has one boundary component, then the answer is ℚ.

Publisher

World Scientific Pub Co Pte Lt

Subject

Geometry and Topology,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179352531100060X

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