First l²-Cohomology Groups

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dc.contributor.authorEastridge, Samuel Vanceen
dc.contributor.committeechairLinnell, Peter A.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-06-17T08:02:01Zen
dc.date.available2015-06-17T08:02:01Zen
dc.date.issued2015-06-15en
dc.description.abstractWe want to take a look at the first cohomology group H^1(G, l^2(G)), in particular when G is locally-finite. First, though, we discuss some results about the space H^1(G, C G) for G locally-finite, as well as the space H^1(G, l^2(G)) when G is finitely generated. We show that, although in the case when G is finitely generated the embedding of C G into l^2(G) induces an embedding of the cohomology groups H^1(G, C G) into H^1(G, l^2(G)), when G is countably-infinite locally-finite, the induced homomorphism is not an embedding. However, even though the induced homomorphism is not an embedding, we still have that H^1(G, l^2(G)) neq 0 when G is countably-infinite locally-finite. Finally, we give some sufficient conditions for H^1(G,l^2(G)) to be zero or non-zero.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:5239en
dc.identifier.urihttp://hdl.handle.net/10919/52952en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectGroup Cohomologyen
dc.subjectUncountableen
dc.subjectAmenableen
dc.subjectLocally Finiteen
dc.titleFirst l²-Cohomology Groupsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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