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The cobordism group of homology cylinders
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Cha, Jae Choon, Friedl, Stefan and Kim, Taehee (2011) The cobordism group of homology cylinders. Compositio Mathematica, Vol.147 (No.3). pp. 914-942. doi:10.1112/S0010437X10004975 ISSN 0010-437X.
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Official URL: http://dx.doi.org/10.1112/S0010437X10004975
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Homology theory, Cobordism theory, Abelian groups | ||||
Journal or Publication Title: | Compositio Mathematica | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0010-437X | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.147 | ||||
Number: | No.3 | ||||
Page Range: | pp. 914-942 | ||||
DOI: | 10.1112/S0010437X10004975 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 18 December 2015 | ||||
Date of first compliant Open Access: | 18 December 2015 | ||||
Funder: | National Research Foundation of Korea (NRF), Korea (South). Kyoyuk Kwahak Kisulbu [Ministry of Education, Science and Technology] (MEST) | ||||
Grant number: | 2007-0054656 (NRF), 2009-0094069 (NRF), 2009-0068877 (NRF), 2009-0086441 (NRF) |
Data sourced from Thomson Reuters' Web of Knowledge
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