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Ornate necklaces and the homology of the genus one mapping class group
Author(s) -
Conant James
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm076
Subject(s) - mathematics , homology (biology) , mapping class group , combinatorics , pure mathematics , singular homology , group algebra , class (philosophy) , algebra over a field , surface (topology) , topology (electrical circuits) , geometry , biology , artificial intelligence , gene , computer science , genetics
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 inH k ( M 1 k Q )S kfor all k ⩾ 5 satisfying k ≡ 1 mod 4. Here M 1 kis the mapping class group of a genus one surface with k punctures.