of 3-manifold groups
the contents are the following:
- Motivations, definitions and basic results on the reduced
projective class group and the Whitehead group. Some computations.
- Statements and some discussions on the results of Waldhausen
(Whitehead group of fundamental group of Haken 3-manifolds), Stallings
(Whitehead group for free products), Farrell-Jones (Whitehead group of
fundamental group of nonpositively curved manifolds), Farrell-Hsiang
(Whitehead group of poly-cyclic groups) and Plotnick (Whitehead group
of fundamental group of non-Haken Seifert fibered spaces).
- Statement of the Geometrization Conjecture for aspherical
- Finally putting together the above results we deduce that the
Whitehead group and the lower K-groups
all vanish for the fundamental group of any torsion free 3-manifold
group provided we assume the Geometrization conjecture.
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