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1201  HĂ¶lder Compactification for Some Manifolds with Pinched Negative Curvature Near Infinity Bahuaud, Eric; Marsh, Tracey
We consider a complete noncompact Riemannian manifold $M$ and give
conditions on a compact submanifold $K \subset M$ so that the outward
normal exponential map off the boundary of $K$ is a diffeomorphism
onto $\MlK$. We use this to compactify $M$ and show that pinched
negative sectional curvature outside $K$ implies $M$ has a
compactification with a welldefined H\"older structure independent of
$K$. The H\"older constant depends on the ratio of the curvature
pinching. This extends and generalizes a 1985 result of Anderson and
Schoen.


1219  CR Extension from Manifolds of Higher Type Baracco, Luca; Zampieri, Giuseppe
This paper deals with the extension of CR functions
from a manifold $M\subset \mathbb C^n$ into directions produced by higher
order commutators of holomorphic and antiholomorphic vector fields. It
uses the theory of complex ``sectors'' attached to real submanifolds
introduced in recent joint work of the authors with D. Zaitsev. In
addition, it develops a new technique of approximation of sectors by
smooth discs.


1240  Categorification of the Colored Jones Polynomial and Rasmussen Invariant of Links Beliakova, Anna; Wehrli, Stephan
We define a family of formal Khovanov brackets
of a colored link depending on two parameters.
The isomorphism classes of these brackets are
invariants of framed colored links.
The BarNatan functors applied to these brackets
produce Khovanov and Lee homology theories categorifying the colored
Jones polynomial. Further,
we study conditions under which
framed colored link cobordisms induce chain transformations between
our formal brackets. We conjecture that
for special choice of parameters, Khovanov and Lee homology theories
of colored links are functorial (up to sign).
Finally, we extend the Rasmussen invariant to links and give examples
where this invariant is a stronger obstruction to sliceness
than the multivariable LevineTristram signature.


1267  Nonadjacent Radix$\tau$ Expansions of Integers in Euclidean Imaginary Quadratic Number Fields Blake, Ian F.; Murty, V. Kumar; Xu, Guangwu
In his seminal papers, Koblitz proposed curves
for cryptographic use. For fast operations on these curves,
these papers also
initiated a study of the radix$\tau$ expansion of integers in the number
fields $\Q(\sqrt{3})$ and $\Q(\sqrt{7})$. The (window)
nonadjacent form of $\tau$expansion of integers in
$\Q(\sqrt{7})$ was first investigated by Solinas.
For integers in $\Q(\sqrt{3})$, the nonadjacent form
and the window nonadjacent form of the $\tau$expansion were
studied. These are used for efficient
point multiplications on Koblitz curves.
In this paper, we complete
the picture by producing the (window)
nonadjacent radix$\tau$ expansions
for integers in all Euclidean imaginary quadratic number fields.


1283  Remarks on LittlewoodPaley Analysis Ho, KwokPun
LittlewoodPaley analysis is generalized in
this article. We show that the compactness of the Fourier support
imposed on the analyzing function can be removed. We also prove
that the LittlewoodPaley decomposition of tempered distributions
converges under a topology stronger than the weakstar topology,
namely, the inductive limit topology. Finally, we construct a
multiparameter LittlewoodPaley analysis and obtain the
corresponding ``renormalization'' for the convergence of this
multiparameter LittlewoodPaley analysis.


1306  Theta Lifts of Tempered Representations for Dual Pairs $(\Sp_{2n}, O(V))$ Mui\'c, Goran
This paper is the continuation of our previous work on the explicit
determination of the structure of theta lifts for dual pairs
$(\Sp_{2n}, O(V))$ over a nonarchimedean field $F$ of characteristic
different than $2$, where $n$ is the split rank of $\Sp_{2n}$ and the
dimension of the space $V$ (over $F$) is even. We determine the
structure of theta lifts of tempered representations in terms of theta
lifts of representations in discrete series.


1336  Moving Frames for Lie PseudoGroups Olver, Peter J.; Pohjanpelto, Juha
We propose a new, constructive theory of moving frames for Lie
pseudogroup actions on submanifolds. The moving frame provides an
effective means for determining complete systems of differential
invariants and invariant differential forms, classifying their
syzygies and recurrence relations, and solving equivalence and
symmetry problems arising in a broad range of applications.


1387  On $n$Dimensional Steinberg Symbols Romo, Fernando Pablos
The aim of this work is to provide a new approach for constructing
$n$dimensional Steinberg symbols on discrete valuation fields from
$(n+1)$cocycles and to study reciprocity laws on curves related to
these symbols.


1406  Hauteur asymptotique des points de Heegner Ricotta, Guillaume; Vidick, Thomas
Geometric intuition suggests that the N\'{e}ronTate height of Heegner
points on a rational elliptic curve $E$ should be asymptotically
governed by the degree of its modular parametrisation. In this paper,
we show that this geometric intuition asymptotically holds on average
over a subset of discriminants. We also study the asymptotic behaviour
of traces of Heegner points on average over a subset of discriminants
and find a difference according to the rank of the elliptic curve. By
the GrossZagier formulae, such heights are related to the special
value at the critical point for either the derivative of the
RankinSelberg convolution of $E$ with a certain weight one theta
series attached to the principal ideal class of an imaginary quadratic
field or the twisted $L$function of $E$ by a quadratic Dirichlet
character. Asymptotic formulae for the first moments associated with
these $L$series and $L$functions are proved, and experimental results
are discussed. The appendix contains some conjectural applications of
our results to the problem of the discretisation of odd quadratic
twists of elliptic curves.


1437  Author Index  Index des auteurs CJM
No abstract.

