caa a22 4500 445884126 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9540-5 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9540-5 Abelian quotients of monoids of homology cylinders [Elektronische Daten] [Hiroshi Goda, Takuya Sakasai] A homology cylinder over a surface consists of a homology cobordism between two copies of the surface and markings of its boundary. The set of isomorphism classes of homology cylinders over a fixed surface has a natural monoid structure and it is known that this monoid can be seen as an enlargement of the mapping class group of the surface. We now focus on abelian quotients of this monoid. We show that both the monoid of all homology cylinders and that of irreducible homology cylinders are not finitely generated and moreover they have big abelian quotients. These properties contrast with the fact that the mapping class group is perfect in general. The proof is given by applying sutured Floer homology theory to homologically fibered knots studied in a previous paper. Springer Science+Business Media B.V., 2010 Homology cylinder nationallicence Homology cobordism nationallicence Sutured manifold nationallicence Sutured Floer homology nationallicence Goda Hiroshi Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, 184-8588, Tokyo, Japan aut Sakasai Takuya Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, 152-8551, Tokyo, Japan aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 387-396 0046-5755 151:1<387 2011 151 10711 https://doi.org/10.1007/s10711-010-9540-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9540-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goda Hiroshi Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, 184-8588, Tokyo, Japan aut NATIONALLICENCE 700 1- Sakasai Takuya Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, 152-8551, Tokyo, Japan aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 387-396 0046-5755 151:1<387 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer