Fukaya categories of the torus and Dehn surgery

This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of this theory: the invariants of 3-manifolds bounding S^2 union T^2, regarded as modules over the Fukaya category of the punctured 2-torus. We extract a short proof of exactness of the Dehn surgery triangle in Heegaard Floer homology. We show that A-infinity structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category of the punctured 2-torus are governed by just two parameters (m^6,m^8), extracted from the Hochschild cohomology of A. For the Fukaya category itself, m^6 is nonzero.Comment: 29 pages, 2 figures, a footnote adde

Prevalence of prostate cancer in high boron-exposed population: A community-based study

We investigated the possible relationship between boron exposure and prostate cancer (PCa) for men living and being employed at boron mines in villages with rich boron minerals. Out of 456 men studied, 159 were from villages with rich boron sources and boron levels in drinking water of >1 mg L -1 and these men formed the study group, while 63 from villages with rich boron sources and boron levels in drinking water of <1 mg L -1 were enrolled into control group 1. A further 234 subjects from other villages with no boron mines were considered as control group 2. Prostate specific antigen (PSA) levels could be obtained from a total of 423 men. Urinary boron concentration as an indicator of boron exposure in 63 subjects, prostatic volumes by transrectal ultrasonography in 39 subjects, and prostatic biopsies in 36 subjects were obtained for study and control groups. The daily boron exposure was calculated according to urinary boron levels. Although there was no significant difference among the groups in terms of total PSA levels, the number of subjects with tPSA ?2.5 and tPSA ?10.0 ng dL -1 prostatic volumes in men whose prostates were biopsied (p<0.012) was significantly lower in the study group as compared with those in the control group 2. These results suggested that high exposure to boron might have an implication within the prostatic cellular processes related to hyperplasia and carcinogenesis, even though we did not find a statistically significant association between PCa and boron exposure. © Springer Science+Business Media, LLC 2011.This research was supported by the National Boron Research Institute, grant no. AR-GE/6

Poisson Structures on Smooth 4–Manifolds

We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector has rank 0 on the singularities, where we give its local form explicitly.Comment: v3: 17pgs. We shortened, and streamlined, both the proof and the exposition. The main result now follows from a formula used by Damianou-Petalidou, attributed to Flaschka-Rati