Search results for "geometry and topology"
showing 10 items of 457 documents
On the graded identities and cocharacters of the algebra of 3×3 matrices
2004
Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the grade…
The cohomology of a variation of polarized Hodge structures over a quasi-compact Kähler manifold
2007
In this article, we consider the cohomologies with coefficients in a variation of polarized Hodge structures on a quasi-compact Kaehler manifold. We show that the L 2 L^2 -Dolbeault cohomology can be identified with the L 2 L^2 cohomology; we also give several direct applications of the result above.
On Hodge theory for the generalized geometry (I)
2013
Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.
The “λ-medial axis”
2005
Medial axis is known to be unstable for nonsmooth objects. For an open set O, we define the weak feature size, wfs, minimum distance between Oc and the critical points of the function distance to Oc. We introduce the "lambda-medial axis" Mλ of O, a subset of the medial axis of O which captures the homotopy type of O when λ < wfs. We show that, at least for some "regular" values of λ, Mλ remains stable under Hausdorff distance perturbations of Oc.
FRACTALITY EVIDENCE AND LONG-RANGE DEPENDENCE ON CAPITAL MARKETS: A HURST EXPONENT EVALUATION
2014
Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is…
Non-equivalent hyperbolic knots
2002
We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist. 2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50
Uniform continuity of quasiconformal mappings and conformal deformations
2008
We prove that quasiconformal maps onto domains satisfying a suitable growth condition on the quasihyperbolic metric are uniformly continuous even when both domains are equipped with internal metric. The improvement over previous results is that the internal metric can be used also in the image domain. We also extend this result for conformal deformations of the euclidean metric on the unit ball of R n \mathbb {R}^n .
Lenses on very curved zones of a singular foliation of C2
2018
Abstract We renormalize, using suitable lenses, small domains of a singular holomorphic foliation of C 2 where the curvature is concentrated. At a proper scale, the leaves are almost translates of a graph that we will call profile. When the leaves of the foliations are levels f = λ , where f is a polynomial in 2 variables, this graph is polynomial. Finally we will indicate how our methods may be adapted to study levels of polynomials and 1-forms in C 3 .
Degenerate Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation and the degenerate rational case
2021
International audience; We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV equation given in terms of Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, Fredholm determinants and wronskians. This gives the bridge between the algebro-geometric approach and the Darboux dressing method.We construct also multi-parametric degenerate rational solutions of this equation.
Khovanov homology for signed divides
2009
The purpose of this paper is to interpret polynomial invariants of strongly invertible links in terms of Khovanov homology theory. To a divide, that is a proper generic immersion of a finite number of copies of the unit interval and circles in a [math] –disc, one can associate a strongly invertible link in the [math] –sphere. This can be generalized to signed divides: divides with [math] or [math] sign assignment to each crossing point. Conversely, to any link [math] that is strongly invertible for an involution [math] , one can associate a signed divide. Two strongly invertible links that are isotopic through an isotopy respecting the involution are called strongly equivalent. Such isotopi…