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    Title      l  Free groups in the second bounded cohology
    Author   l  Heesook Park
    Date   l  2009-09-07
    Category   l  ASARC-Preprint-09-23
    Download    l 1297300805_0.295373.pdf  
Abstract. The second bounded cohomology of a free group of
rank greater than 1 is in nite dimensional as a vector space over
R [4]. For a group G and its n-th commutator subgroup G(n), the
quotient G=G(n) is amenable and the homomorphism bH 2(G) !
bH
2(G(n)) induced from the inclusion homomorphism G(n) ! G is
injective. In this paper, we prove that if G(n) is free of rank greater
than 1 for some nite ordinal n, then G is residually solvable and
its second bounded cohomology is in nite 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 1X are given.

Keyword

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