2 resultados para Almost Contact Manifold
em Duke University
Resumo:
For any Legendrian knot in R^3 with the standard contact structure, we show that the existence of an augmentation to any field of the Chekanov-Eliashberg differential graded algebra over Z[t,t^{-1}] is equivalent to the existence of a normal ruling of the front diagram, generalizing results of Fuchs, Ishkhanov, and Sabloff. We also show that any even graded augmentation must send t to -1.
We extend the definition of a normal ruling from J^1(S^1) given by Lavrov and Rutherford to a normal ruling for Legendrian links in #^k(S^1\times S^2). We then show that for Legendrian links in J^1(S^1) and #^k(S^1\times S^2), the existence of an augmentation to any field of the Chekanov-Eliashberg differential graded algebra over Z[t,t^{-1}] is equivalent to the existence of a normal ruling of the front diagram. For Legendrian knots, we also show that any even graded augmentation must send t to -1. We use the correspondence to give nonvanishing results for the symplectic homology of certain Weinstein 4-manifolds.
Resumo:
Knowing one's HIV status is particularly important in the setting of recent tuberculosis (TB) exposure. Blood tests for assessment of tuberculosis infection, such as the QuantiFERON Gold in-tube test (QFT; Cellestis Limited, Carnegie, Victoria, Australia), offer the possibility of simultaneous screening for TB and HIV with a single blood draw. We performed a cross-sectional analysis of all contacts to a highly infectious TB case in a large meatpacking factory. Twenty-two percent were foreign-born and 73% were black. Contacts were tested with both tuberculin skin testing (TST) and QFT. HIV testing was offered on an opt-out basis. Persons with TST >or=10 mm, positive QFT, and/or positive HIV test were offered latent TB treatment. Three hundred twenty-six contacts were screened: TST results were available for 266 people and an additional 24 reported a prior positive TST for a total of 290 persons with any TST result (89.0%). Adequate QFT specimens were obtained for 312 (95.7%) of persons. Thirty-two persons had QFT results but did not return for TST reading. Twenty-two percent met the criteria for latent TB infection. Eighty-eight percent accepted HIV testing. Two (0.7%) were HIV seropositive; both individuals were already aware of their HIV status, but one had stopped care a year previously. None of the HIV-seropositive persons had latent TB, but all were offered latent TB treatment per standard guidelines. This demonstrates that opt-out HIV testing combined with QFT in a large TB contact investigation was feasible and useful. HIV testing was also widely accepted. Pairing QFT with opt-out HIV testing should be strongly considered when possible.