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• W3100360537 abstract "Abstract Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as an enlargement of the mapping class group. Using torsion invariants, we show that the abelianization of this group is infinitely generated provided that the first Betti number of the surface is positive. In particular, this shows that the group is not perfect. This answers questions of Garoufalidis and Levine, and Goda and Sakasai. Furthermore, we show that the abelianization of the group has infinite rank for the case that the surface has more than one boundary component. These results also hold for the homology cylinder analogue of the Torelli group." @default.
• W3100360537 created "2020-11-23" @default.
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• W3100360537 date "2010-09-07" @default.
• W3100360537 modified "2023-10-17" @default.
• W3100360537 title "The cobordism group of homology cylinders" @default.
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• W3100360537 doi "https://doi.org/10.1112/s0010437x10004975" @default.
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