628 research outputs found
Smooth free involution of and Smith conjecture for imbeddings of in
This paper establishes an equivalence between existence of free involutions
on and existence of involutions on with fixed point set an
imbedded , then a family of counterexamples of the Smith conjecture for
imbeddings of in are given by known result on . 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 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
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
Twisted equivariant K-theory with complex coefficients
Using a global version of the equivariant Chern character, we describe the
complexified twisted equivariant K-theory of a space with a compact Lie group
action in terms of fixed-point data. We apply this to the case of a compact Lie
group acting on itself by conjugation, and relate the result to the Verlinde
algebra and to the Kac numerator at q=1. Verlinde's formula is also discussed
in this context.Comment: Final version, to appear in Topology. Exposition improved, rational
homotopy calculation completely rewritte
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.
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