A note on the abelianizations of finiteindex subgroups of the mapping class group
Author:
Andrew Putman
Journal:
Proc. Amer. Math. Soc. 138 (2010), 753758
MSC (2000):
Primary 57XX; Secondary 20XX
Published electronically:
September 30, 2009
MathSciNet review:
2557192
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Abstract: For some , let be a finite index subgroup of the mapping class group of a genus surface (possibly with boundary components and punctures). An old conjecture of Ivanov says that the abelianization of should be finite. In the paper we prove two theorems supporting this conjecture. For the first, let denote the Dehn twist about a simple closed curve . For some , we have . We prove that is torsion in the abelianization of . Our second result shows that the abelianization of is finite if contains a ``large chunk'' (in a certain technical sense) of the Johnson kernel, that is, the subgroup of the mapping class group generated by twists about separating curves.
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Additional Information
Andrew Putman
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 2306, 77 Massachusetts Avenue, Cambridge, Massachusetts 021394307
Email:
andyp@math.mit.edu
DOI:
http://dx.doi.org/10.1090/S0002993909101247
Received by editor(s):
February 3, 2009
Received by editor(s) in revised form:
May 19, 2009
Published electronically:
September 30, 2009
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
