The second bounded cohomology of 3-manifolds (Q1848502)

The authors determine the second bounded cohomology of certain 3-manifold groups. By a theorem of Gromov, this yields the singular second bounded cohomology of the corresponding manifolds themselves. More precisely, the authors study those compact orientable 3-manifolds whose fundamental group admits a non-trivial decomposition as an amalgamated product. The main result is that for such groups, the second bounded cohomology is infinite dimensional unless the group is virtually solvable. This result relies among other things on a result of the first author for general amalgamated products [Trans. Am. Math. Soc. 352, No. 3, 1113-1129 (2000; Zbl 1053.20517)]. A more precise statement is given, making use of the structure theory of 3-manifolds without 2-spheres in the boundary. In fact, this more precise statement would be a complete description if Thurston's geometrization conjecture holds.