  We give lower bounds on the maximal injectivity radius for a closed
orientable hyperbolic 3-manifold M with first Betti number 2, under some
additional topological hypotheses. A corollary of the main result is that if M
has first Betti number 2 and contains no fibroid surface then its maximal
injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed,
with no topological restrictions, that the maximal injectivity radius exceeds
arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti
number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The
proof combines a result due to Przeworski with techniques developed by the
authors in the 1990s.
