Smooth free involution of HCP3H{\Bbb C}P^3 and Smith conjecture for imbeddings of S3S^3 in S6S^6

This paper establishes an equivalence between existence of free involutions on $H{\Bbb C}P^3$ and existence of involutions on $S^6$ with fixed point set an imbedded $S^3$, then a family of counterexamples of the Smith conjecture for imbeddings of $S^3$ in $S^6$ are given by known result on $H{\Bbb C}P^3$. In addition, this paper also shows that every smooth homotopy complex projective 3-space admits no orientation preserving smooth free involution, which answers an open problem [Pe]. Moreover, the study of existence problem for smooth orientation preserving involutions on $H{\Bbb C}P^3$ is completed.Comment: 10 pages, final versio

Sea ice - atmosphere interaction: Application of multispectral satellite data in polar surface energy flux estimates

In the past six months, work has continued on energy flux sensitivity studies, ice surface temperature retrievals, corrections to Advanced Very High Resolution Radiometer (AVHRR) thermal infrared data, modelling of cloud fraction retrievals, and radiation climatologies. We tentatively conclude that the SSM/I may not provide accurate enough estimates of ice concentration and type to improve our shorter term energy flux estimates. SSM/I derived parameters may still be applicable in longer term climatological flux characterizations. We hold promise for a system coupling observation to a ice deformation model. Such a model may provide information on ice distribution which can be used in energy flux calculations. Considerable variation was found in modelled energy flux estimates when bulk transfer coefficients are modulated by lead fetch. It is still unclear what the optimum formulation is and this will be the subject of further work. Data sets for ice surface temperature retrievals were assembled and preliminary data analysis was started. Finally, construction of a conceptual framework for further modelling of the Arctic radiation flux climatology was started

A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of spheres. Let N be a closed connected orientable 3-manifold. Our main result is the following description of the set Emb^6(N) of embeddings N\to R^6 up to isotopy. The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where d(u) is the divisibility of the projection of u to the free part of H_1(N;Z). The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on Emb^6(N) by embedded connected sum. It was proved that the orbit space of this action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's smoothing theory). The new part of our classification result is determination of the orbits of the action. E. g. for N=RP^3 the action is free, while for N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that for each knot l:S^3\to R^6 the embedding f#l is isotopic to f. Our proof uses new approaches involving the Kreck modified surgery theory or the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in Math. Zei

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Contribution of connexins to the function of the vascular wall

Gap junction channels provide an enclosed conduit for direct exchanges of signalling molecules, including ions and small metabolites between cells. This system of communication allows cells to monitor the functional state of their neighbours, and is rapidly modulated to continuously adapt to the immediate needs of groups of coupled cells. In the major arteries, endothelial cells may express three connexins isotypes, namely Connexin 37 (Cx37), Cx40 and Cx43, whereas the underlying smooth muscle cells may express Cx37, Cx40, Cx43 and Cx45. Moreover, myoendothelial gap junctions have also been shown to be involved in the regulation of vascular tone. This review highlights the regulation of vessel connexins in response to injury, as observed during experimental hypertension or wound repair, as well as the consequences of loss of one connexin in different transgenic null mice. In view of the major endocrine role of the kidney in the control of blood pressure, we also discuss the distribution of connexins in the kidney vasculature. Cx40 is present between endothelial cells of vessels and glomeruli, as well as between renin-secreting cells, the modified smooth muscle cells which form the wall of the terminal part of afferent arterioles. Modulation of Cx40 expression in a model of renin-dependent hypertension suggests that this connexin may be implicated in the function of renin-secreting cells. Finally, to address the possible regulation of connexin expression by fluid pressure, we summarize the effects of elevated transmural urine pressure on bladder Cx43 expression

The Lie derivative of spinor fields: theory and applications

Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these structures admit a canonical decomposition of the pull-back vector bundle i_P^*(TQ) = P\times_Q TQ over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, such a decomposition defines an infinitesimal canonical lift. This lift extends to a prolongation Gamma-structure on P. In this general geometric framework the concept of a Lie derivative of spinor fields is reviewed. On specializing to the case of the Kosmann lift, we recover Kosmann's original definition. We also show that in the case of a reductive G-structure one can introduce a "reductive Lie derivative" with respect to a certain class of generalized infinitesimal automorphisms, and, as an interesting by-product, prove a result due to Bourguignon and Gauduchon in a more general manner. Next, we give a new characterization as well as a generalization of the Killing equation, and propose a geometric reinterpretation of Penrose's Lie derivative of "spinor fields". Finally, we present an important application of the theory of the Lie derivative of spinor fields to the calculus of variations.Comment: 28 pages, 1 figur

From double Lie groupoids to local Lie 2-groupoids

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.Comment: 23 pages, a few minor changes, including a correction to Lemma 6.

Geometry of integrable dynamical systems on 2-dimensional surfaces

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions, and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.Comment: 31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamic

Functional significance of repressor element 1 silencing transcription factor (REST) target genes in pancreatic beta cells

Aims/hypothesis: The expression of several neuronal genes in pancreatic beta cells is due to the absence of the transcription factor repressor element 1 (RE-1) silencing transcription factor (REST). The identification of these traits and their functional significance in beta cells has only been partly elucidated. Herein, we investigated the biological consequences of a repression of REST target genes by expressing REST in beta cells. Methods: The effect of REST expression on glucose homeostasis, insulin content and release, and beta cell mass was analysed in transgenic mice selectively expressing REST in beta cells. Relevant target genes were identified in INS-1E and primary beta cells expressing REST. Results: Transgenic mice featuring a beta cell-targeted expression of REST exhibited glucose intolerance and reduced beta cell mass. In primary beta cells, REST repressed several proteins of the exocytotic machinery, including synaptosomal-associated protein (SNAP) 25, synaptotagmin (SYT) IV, SYT VII, SYT IX and complexin II; it impaired first and second phases of insulin secretion. Using RNA interference in INS-1E cells, we showed that SYT IV and SYT VII were implicated in the control of insulin release. Conclusions/interpretation: The data document the critical role of REST target genes in pancreatic beta cells. Specifically, we provide evidence that the downregulation of these genes is detrimental for the exocytosis of large dense core vesicles, thus contributing to beta cell dysfunction and impaired glucose homeostasi