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Cha, Jae Choon, 1971, Friedl, Stefan and Kim, Taehee. (2011) The cobordism group of homology cylinders. Compositio Mathematica, Vol.147 (No.3). pp. 914942. ISSN 0010437X

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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 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of 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:  0010437X 
Date:  2011 
Volume:  Vol.147 
Number:  No.3 
Page Range:  pp. 914942 
Identification Number:  10.1112/S0010437X10004975 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  National Research Foundation of Korea (NRF), Korea (South). Kyoyuk Kwahak Kisulbu [Ministry of Education, Science and Technology] (MEST) 
Grant number:  20070054656 (NRF), 20090094069 (NRF), 20090068877 (NRF), 20090086441 (NRF) 
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URI:  http://wrap.warwick.ac.uk/id/eprint/39993 
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