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Bulletin of the London Mathematical Society Advance Access originally published online on September 28, 2007
Bulletin of the London Mathematical Society 2007 39(6):881-891; doi:10.1112/blms/bdm076
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© 2007 London Mathematical Society

Ornate necklaces and the homology of the genus one mapping class group

James Conant

Department of Mathematics
University of Tennessee
Knoxville, TN 37996
USA

Received 31 October 2006. Revision received 15 May 2007.

According to seminal work of Kontsevich, the unstable homology of the mapping class group of a surface can be computed via the homology of a certain Lie algebra. In a recent paper, S. Morita analyzed the abelianization of this Lie algebra, thereby constructing a series of candidates for unstable classes in the homology of the mapping class group. In the current paper, we show that these cycles are all nontrivial, representing homology classes in Formula for all k ≥ 5 satisfying k {equiv} 1 mod 4. Here Formula is the mapping class group of a genus one surface with k punctures.

Correspondence: jconant{at}math.utk.edu

2000 Mathematics Subject Classification 17B40, 17B56, 32G15.


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