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- W2963470135 abstract "Morita introduced in 2008 a [Formula: see text]-cocycle on the group of homology cobordisms of surfaces with values in an infinite-dimensional vector space. His [Formula: see text]-cocycle contains all the “traces” of Johnson homomorphisms which he introduced 15 years earlier in his study of the mapping class group. In this paper, we propose a new version of Morita’s [Formula: see text]-cocycle based on a simple and explicit construction. Our [Formula: see text]-cocycle is proved to satisfy several fundamental properties, including a connection with the Magnus representation and the LMO homomorphism. As an application, we show that the rational abelianization of the group of homology cobordisms is non-trivial. Besides, we apply some of our algebraic methods to compare two natural filtrations on the automorphism group of a finitely-generated free group." @default.
- W2963470135 created "2019-07-30" @default.
- W2963470135 creator A5064609147 @default.
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- W2963470135 date "2018-10-10" @default.
- W2963470135 modified "2023-10-14" @default.
- W2963470135 title "Morita’s trace maps on the group of homology cobordisms" @default.
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- W2963470135 doi "https://doi.org/10.1142/s179352531950064x" @default.
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