K-theory of 3-manifold groups

Contents: Roughly 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 3-manifolds.
• 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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