Tenseness of Riemannian flows

We show that any transversally complete Riemannian foliation F of dimension one on any possibly non-compact manifold M is tense; namely, (M,F) admits a Riemannian metric such that the mean curvature form of F is basic. This is a partial generalization of a result of Dominguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Dominguez. As an application, we generalize some well known results including Masa's characterization of tautness.Comment: 14 pages. Accepted for publication in Annales de l'Institut Fourier. We have performed some changes in this final version, following the suggestions of the referee. Among other changes, several typos and the proof of Theorem 1.4 have been correcte

Equivariant intersection cohomology of the circle actions

Accepté pour publication au RCSM: Real Academia de Ciencias Exactas, Fisicas y Naturales.In this paper, we prove that the orbit space $B$ and the Euler class of the action \Phi \colon \sbat \times X \to X determine both the equivariant intersection cohomology of the pseudomanifold $X$ and its localization. We also construct a spectral sequence converging to the equivariant intersection cohomology of $X$ whose third term is described in terms of the intersection cohomology of $B$

The Gysin braid for S3S^3-actions on manifolds

Given a smooth action of the sphere $\mathbb S^3$ on a manifold $M$, we have previously constructed a Gysin sequence relating the cohomology of the manifold $M$ and that of the orbit space $M/\mathbb S^3$. This sequence involves an exotic term depending on the subset $M^{\mathbb S^1}$. Notice that the orbit space is a stratified pseudomanifold, a kind of singular spaces where intersection cohomology applies. In the case where the the action is semi-free, the first author has already constructed a Gysin sequence relating the cohomology of $M$ and the intersection cohomology of $M/\mathbb S^3$. What happens if the action is not semi-free? This is the goal of this work. The situation is more complicated and we do not find a Gysin sequence but a Gysin braid relating the cohomology of $M$ and the intersection cohomology of $M/\mathbb S^3$. This braid also contains an exotic term depending this time on the intersection cohomology of $M^{\mathbb S^1}$

Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Treatment variability and its relationships to outcomes among patients with Wernicke's encephalopathy: A multicenter retrospective study

Background: Despite guidelines and recommendations, Wernicke's encephalopathy (WE) treatment lacks evidence, leading to clinical practice variability.Aims: Given the overall lack of information on thiamine use for WE treatment, we analyzed data from a large, well-characterized multicenter sample of patients with WE, examining thiamine dosages; factors associated with the use of different doses, frequencies, and routes; and the influence of differences in thiamine treatment on the outcome.Methods: This retrospective study was conducted with data from 443 patients from 21 centers obtained from a nationwide registry of the Spanish Society of Internal Medicine (from 2000 to 2012). Discharge codes and Caine criteria were applied for WE diagnosis, and treatment-related (thiamine dosage, frequency, and route of administration) demographic, clinical, and outcome variables were analyzed.Results: We found marked variability in WE treatment and a low rate of high-dose intravenous thiamine administration. Seventy-eight patients out of 373 (20.9%) received > 300 mg/day of thiamine as initial dose. Patients fulfilling the Caine criteria or presenting with the classic WE triad more frequently received parenteral treatment. Delayed diagnosis (after 24 h hospitalization), the fulfillment of more than two Caine criteria at diagnosis, mental status alterations, and folic acid deficiency were associated significantly with the lack of complete recovery. Malnutrition, reduced consciousness, folic acid deficiency, and the lack of timely thiamine treatment were risk factors for mortality.Conclusions: Our results clearly show extreme variability in thiamine dosages and routes used in the management of WE. Measures should be implemented to ensure adherence to current guidelines and to correct potential nutritional deficits in patients with alcohol use disorders or other risk factors for WE

Hard Lefschetz property for S3\mathbb{S}^3-actions

8 pagesThe Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus generalizing what happens in the important cases of both K-contact and Sasakian manifolds. In this work we define both versions of the HLP for almost-free S3 -actions, and prove that they agree for actions satisfying a cohomological condition, which includes the important category of 3-Sasakian manifolds, where those two versions of the HLP are shown to be held. We also provide a family of examples of free actions of the 3-sphere which are not 3-Sasakian manifolds, but satisfy the HLP