First l²-Cohomology Groups

We 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2015

Author dc:creator

• Eastridge, Samuel Vance

Chair dc:contributor.committeechair

• Linnell, Peter A.

Committee members dc:contributor.committeemember

• Ball, Joseph A.
• Mihalcea, Constantin Leonardo

• Group Cohomology
• Uncountable
• Amenable
• Locally Finite

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:5239

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/52952