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This book discusses the necessary tools to compute
the lower algebraic K-theory of the integral group
ring for the pure braid groups on the 2- sphere and
on the real projective plane. We begin with the
statement of the fibered isomorphism conjecture of
Farrell-Jones through the definitions of all
necessary ingredients for the actual computations. We
illustrate the defnitions with specific examples used
later on to discuss the proof of the main results of
this work.
Consider the 2- sphere or the real projective plane
and let PBn(M) and Bn(M) be the pure and the full
braid groups on n-strands of M respectively. In this
work we show that PBn(M) and Bn(M) satisfy the
Farrell-Jones isomorphism conjecture and use this
fact to compute the lower algebraic K-groups for the
integral group ring Z[PBn(M)].
the lower algebraic K-theory of the integral group
ring for the pure braid groups on the 2- sphere and
on the real projective plane. We begin with the
statement of the fibered isomorphism conjecture of
Farrell-Jones through the definitions of all
necessary ingredients for the actual computations. We
illustrate the defnitions with specific examples used
later on to discuss the proof of the main results of
this work.
Consider the 2- sphere or the real projective plane
and let PBn(M) and Bn(M) be the pure and the full
braid groups on n-strands of M respectively. In this
work we show that PBn(M) and Bn(M) satisfy the
Farrell-Jones isomorphism conjecture and use this
fact to compute the lower algebraic K-groups for the
integral group ring Z[PBn(M)].