DC Field | Value | Language |
---|---|---|
dc.contributor.author | Park, HeeSook | ko |
dc.date.accessioned | 2013-03-12T15:50:36Z | - |
dc.date.available | 2013-03-12T15:50:36Z | - |
dc.date.created | 2012-07-03 | - |
dc.date.created | 2012-07-03 | - |
dc.date.issued | 2012 | - |
dc.identifier.citation | COMMUNICATIONS IN ALGEBRA, v.40, no.4, pp.1390 - 1412 | - |
dc.identifier.issn | 0092-7872 | - |
dc.identifier.uri | http://hdl.handle.net/10203/102779 | - |
dc.description.abstract | The second bounded cohomology of a free group of rank greater than 1 is infinite dimensional as a vector space over R [ 4]. For a group G and its nth commutator subgroup G((n)), the quotient G/G((n)) is amenable and the homomorphism (H) over cap (2)(G) --> (H) over cap (2)(G((n))) induced from the inclusion homomorphism G((n)) --> G is injective.In this article, we prove that if G((n)) is free of rank greater than 1 for some finite ordinal n, then G is residually solvable and its second bounded cohomology is infinite dimensional. We prove its converse for a group generated by two elements. As for groups that are not residually solvable, we investigate the dimension of the second bounded cohomology of a perfect group. Also, some results on bounded cohomology of a connected CW complex X by applying a Quillen's plus construction X+ to kill a perfect normal subgroup of pi X-1 are given. | - |
dc.language | English | - |
dc.publisher | TAYLOR & FRANCIS INC | - |
dc.title | FREE GROUPS IN THE SECOND BOUNDED COHOMOLOGY | - |
dc.type | Article | - |
dc.identifier.wosid | 000304276200015 | - |
dc.identifier.scopusid | 2-s2.0-84859862358 | - |
dc.type.rims | ART | - |
dc.citation.volume | 40 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 1390 | - |
dc.citation.endingpage | 1412 | - |
dc.citation.publicationname | COMMUNICATIONS IN ALGEBRA | - |
dc.identifier.doi | 10.1080/00927872.2010.551684 | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Free groups | - |
dc.subject.keywordAuthor | Perfect groups | - |
dc.subject.keywordAuthor | Residually solvable groups | - |
dc.subject.keywordAuthor | The second bounded cohomology | - |
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