2011年4月
Abelian quotients of monoids of homology cylinders
GEOMETRIAE DEDICATA
- ,
- 巻
- 151
- 号
- 1
- 開始ページ
- 387
- 終了ページ
- 396
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s10711-010-9540-5
- 出版者・発行元
- SPRINGER
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.
- リンク情報
- ID情報
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- DOI : 10.1007/s10711-010-9540-5
- ISSN : 0046-5755
- Web of Science ID : WOS:000288390900025