On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups

http://arxiv.org/PS_cache/math/pdf/9810/9810034v1.pdfA gauge theoretic description of the Morgan-Shalen compactification of the SL(2, C) character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space of Higgs bundles via the Hitchin map

Surface groups acting on CAT(−1) spaces

Harmonic map theory is used to show that a convex cocompact surface group action on a CAT(-1) metric space fixes a convex copy of the hyperbolic plane (i.e. the action is Fuchsian) if and only if the Hausdorff dimension of the limit set of the action is equal to 1. This provides another proof of a result of Bonk and Kleiner. More generally, we show that the limit set of every convex cocompact surface group action on a CAT(-1) space has Hausdorff dimension ≥1, where the inequality is strict unless the action is Fuchsian

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Carotid ultrasound findings as a predictor of long-term survival after abdominal aortic aneurysm repair: a 14-year prospective study

AbstractPurposeSeveral factors have been related to long-term survival after open abdominal aortic aneurysm (AAA) repair. The effect of carotid stenosis on outcome has not yet been examined. We performed an open prospective study to evaluate the prognostic significance of carotid stenosis on long-term survival of patients who had undergone elective operative repair of AAA.MethodsTwo hundred eight patients who underwent elective open AAA repair in our department between March 1987 and December 2001 were included in the study. All patients were evaluated preoperatively with color duplex ultrasound (US) scanning of the carotid arteries, and were followed up with clinical examination and carotid duplex US scanning 1 month after the operation and every 6 months thereafter. Median duration of follow-up was 50 months (range, 5-181 months). Cardiovascular morbidity and mortality, as well as all causes of mortality, were recorded and analyzed with regard to traditional risk factors and carotid US findings.ResultsTwenty-seven fatal and 46 nonfatal cardiovascular events were recorded. Both univariate and multivariate analysis showed that carotid stenosis 50% or greater and echolucent plaque were significantly associated with cardiovascular mortality and morbidity. Carotid stenosis was a stronger predictor of cardiovascular death than was ankle/brachial index. Age, hypercholesterolemia, coronary artery disease, and diabetes mellitus were also associated with higher mortality and morbidity from cardiovascular causes.ConclusionPatients electively operated on for AAA repair and with stenosis 50% or greater and echolucent plaque at duplex US scanning are at significantly increased risk for cardiovascular mortality and morbidity. Carotid US can therefore be used to select a subgroup of patients with AAA who might benefit from medical intervention, including antiplatelet and lipid-lowering agents

Canalicular adenoma with unicystic morphology. A rare entity

Canalicular adenoma (CA) is a benign salivary gland tumor (SGT) almost exclusively affecting the minor salivary glands, predominantly of the upper lip, and exhibiting characteristic histopathologic features. As observed in several other SGTs, a commonly

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

The clinical significance of soluble E-cadherin in nonsmall cell lung cancer

Aim: Aberrant expression of the epithelial transmembrane adhesion molecule E-cadherin (E-cad) has been associated with many human malignancies. In the present study the clinical significance of serum levels of soluble E-cadherin (sE-cad) in newly diagnosed patients with non small cell lung cancer (NSCLC) was investigated. Material and Methods: An enzyme linked immunospecific assay (ELISA) to determine the circulating levels of sE-cad in 20 newly diagnosed patients with NSCLC as well as in 29 healthy volunteers (control group) was used. Results: NSCLC patients exerted increased circulating levels of sE-cad compared with individuals of the control group (p < 0.001). An association was also detected between serum sE-cad levels and the development of distant metastases. On the contrary, no statistically significant correlation could be established with histological type, gender and smoking habits. Patients with increased sE-cad levels at diagnosis had worser outcome, although multivariate analysis failed to demonstrate that sE-cad levels represent an independent prognostic factor of survival. Conclusion: Our data suggest that E-cad plays a role in the pathogenesis of NSCLC. sE-cad levels may be further studied as a potential prognostic biomarker.Цель: нарушения экспрессии трансмембранной молекулы адгезии эпителия Е-кадерина (Е-cad) ассоциированы со злокачеcтвенными новообразованиями у человека. Цель исследования — оценить клиническое значение содержания секретируемого Е-кадерина (sE-cad) в сыворотке крови больных с диагнозом немелкоклеточного рака легкого (НМКРЛ). Материалы и методы: для определения уровня циркулирующего sE-cad в сыворотке крови 20 больных с НМКРЛ и 29 здоровых доноров применили метод ELISA. Результаты: у больных с НМКРЛ выявлено значительное повышение содержания циркулирующего sE-cad в сыворотке крови по сравнению с таковым в контрольной группе (p < 0,001). Установлена связь между уровнем sE-cad в сыворотке крови и появлением периферических метастазов. Не выявлено статистически достоверной корреляции между гистологическим типом опухоли, полом больного и курением. У пациентов с повышенным содержанием sE-cad наблюдалась тенеденция к худшему исходу заболевания, хотя результаты статистического анализа не подтвердили прогностического значения sE-cad. Выводы: полученные данные позволили предположить, что E-cad участвует в патогенезе НМКРЛ. Оценка содержания sE-cad в качестве прогностического биомаркера нуждается в дальнейшем исследовании

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction