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

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

2006-10-04

arxiv.org/abs/math/0610143v1

Bull. Lond. Math. Soc. 39 (2007), no. 6, 881--891

Mathematics

Quantum Algebra

Scientific paper

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.

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