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

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 degree 4k+1 homology classes in the homology of the mapping class group of a genus one surface with 4k+1 punctures.

preprint2006arXivOpen access
James Conant
math.QAmath.GT
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James Conant

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