Prostate cancer: an evolving paradigm.

Since at least the early 1990s, stage and risk migration have been seen in patients with prostate cancer, likely corresponding to the institution of prostate specific antigen (PSA) screening in health systems. Preoperative risk factors, including PSA level and clinical stage, have decreased significantly. These improved prognostic variables have led to a larger portion of men being stratified with low-risk disease, as per the classification of D'Amico and associates. This, in turn, has corresponded with more favorable postoperative variables, including decreased extraprostatic tumor extension and prolonged biochemical-free recurrence rates. The advent of focal therapy is bolstered by findings of increased unilateral disease with decreased tumor volume. Increasingly, targeted or delayed therapies may be possible within the current era of lower risk disease.

The abelianization of the Johnson kernel

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym H 1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic to the infinitesimal Alexander invariant of the associated graded Lie algebra of G. In this setup, we also obtain a precise nilpotence test. © European Mathematical Society 2014.