Mostrando recursos 1 - 20 de 3.404

  1. Index realization for automorphisms of free groups

    Coulbois, Thierry; Lustig, Martin
    For any surface $\Sigma$ of genus $g\geq1$ and (essentially) any collection of positive integers $i_{1},i_{2},\ldots,i_{\ell}$ with $i_{1}+\cdots+i_{\ell}=4g-4$ Masur and Smillie (Comment. Math. Helv. 68 (1993) 289–307) have shown that there exists a pseudo-Anosov homeomorphism $h:\Sigma\to\Sigma$ with precisely $\ell$ singularities $S_{1},\ldots,S_{\ell}$ in its stable foliation $\mathcal{L}$, such that $\mathcal{L}$ has precisely $i_{k}+2$ separatrices raying out from each $S_{k}$. ¶ In this paper, we prove the analogue of this result for automorphisms of a free group ${F}_{N}$, where “pseudo-Anosov homeomorphism” is replaced by “fully irreducible automorphism” and the Gauss–Bonnet equality $i_{1}+\cdots+i_{\ell}=4g-4$ is replaced by the index inequality $i_{1}+\cdots+i_{\ell}\leq2N-2$ from (Duke Math. J. 93 (1998)...

  2. Long turns, INP’s and indices for free group automorphisms

    Coulbois, Thierry; Lustig, Martin
    The goal of this paper is to introduce a new tool, called long turns, which is a useful addition to the train track technology for automorphisms of free groups, in that it allows one to control periodic INPs in a train track map and hence the index of the induced automorphism.

  3. Sufficient conditions for Strassen’s additivity conjecture

    Teitler, Zach
    We give a sufficient condition for the strong symmetric version of Strassen’s additivity conjecture: the Waring rank of a sum of forms in independent variables is the sum of their ranks, and every Waring decomposition of the sum is a sum of decompositions of the summands. We give additional sufficient criteria for the additivity of Waring ranks and a sufficient criterion for additivity of cactus ranks and decompositions.

  4. Preservation of $p$-Poincaré inequality for large $p$ under sphericalization and flattening

    Durand-Cartagena, Estibalitz; Li, Xining
    Li and Shanmugalingam showed that annularly quasiconvex metric spaces endowed with a doubling measure preserve the property of supporting a $p$-Poincaré inequality under the sphericalization and flattening procedures. Because natural examples such as the real line or a broad class of metric trees are not annularly quasiconvex, our aim in the present paper is to study, under weaker hypotheses on the metric space, the preservation of $p$-Poincaré inequalites under those conformal deformations for sufficiently large $p$. We propose the hypotheses used in a previous paper by the same authors, where the preservation of $\infty$-Poincaré inequality has been studied under the...

  5. Abstract convolution function algebras over homogeneous spaces of compact groups

    Ghaani Farashahi, Arash
    This paper presents a systematic study for structure of abstract Banach function $*$-algebras over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $\mu$ be the normalized $G$-invariant measure over the homogeneous space $G/H$ associated to the Weil’s formula and $1\leq p<\infty$. Then we introduce the notions of convolution and involution for the Banach function spaces $L^{p}(G/H,\mu)$.

  6. Thue equations and lattices

    Thunder, Jeffrey Lin
    We consider Diophantine equations of the kind $|F(x,y)|=m$, where $F(X,Y)\in\mathbb{Z}[X,Y]$ is a homogeneous polynomial of degree at least 3 that has non-zero discriminant, $m$ is a fixed positive integer and $x,y$ are relatively prime integer solutions. Our results improve upon previous theorems due to Bombieri and Schmidt and also Stewart. We further provide reasonable heuristics for conjectures of Schmidt and Stewart regarding such equations.

  7. Spectrally unstable domains

    Mendoza, Gerardo A.
    Let $H$ be a separable Hilbert space, $A_{c}:\mathcal{D}_{c}\subset H\to H$ a densely defined unbounded operator, bounded from below, let $\mathcal{D}_{\min}$ be the domain of the closure of $A_{c}$ and $\mathcal{D}_{\max}$ that of the adjoint. Assume that $\mathcal{D}_{\max}$ with the graph norm is compactly contained in $H$ and that $\mathcal{D}_{\min}$ has finite positive codimension in $\mathcal{D}_{\max}$. Then the set of domains of selfadjoint extensions of $A_{c}$ has the structure of a finite-dimensional manifold $\mathfrak{SA}$ and the spectrum of each of its selfadjoint extensions is bounded from below. If $\zeta$ is strictly below the spectrum of $A$ with a given domain $\mathcal{D}_{0}\in\mathfrak{SA}$,...

  8. Boundedness of a family of Hilbert-type operators and its Bergman-type analogue

    Bansah, Justice S.; Sehba, Benoît F.
    In this paper, we first consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the parameters. Second, we consider boundedness properties of a family of positive Bergman-type operators of the upper-half plane. We give necessary and sufficient conditions on the parameters under which these operators are bounded in the upper triangle case.

  9. On metrics of curvature $1$ with four conic singularities on tori and on the sphere

    Eremenko, Alexandre; Gabrielov, Andrei
    We discuss conformal metrics of curvature $1$ on tori and on the sphere, with four conic singularities whose angles are multiples of $\pi$. Besides some general results we study in detail the family of such symmetric metrics on the sphere, with angles $(\pi,3\pi,\pi,3\pi)$. As a consequence we find new Heun’s equations whose general solution is algebraic.

  10. Extending Huppert’s conjecture from non-Abelian simple groups to quasi-simple groups

    Hung, Nguyen Ngoc; Majozi, Philani R.; Tong-Viet, Hung P.; Wakefield, Thomas P.
    We propose to extend a conjecture of Bertram Huppert [Illinois J. Math. 44 (2000) 828–842] from finite non-Abelian simple groups to finite quasi-simple groups. Specifically, we conjecture that if a finite group $G$ and a finite quasi-simple group $H$ with ${\mathrm{Mult}}(H/\mathbf{Z}(H))$ cyclic have the same set of irreducible character degrees (not counting multiplicity), then $G$ is isomorphic to a central product of $H$ and an Abelian group. We present a pattern to approach this extended conjecture and, as a demonstration, we confirm it for the special linear groups in dimensions $2$ and $3$.

  11. Stretching factors, metrics and train tracks for free products

    Francaviglia, Stefano; Martino, Armando
    In this paper, we develop the metric theory for the outer space of a free product of groups. This generalizes the theory of the outer space of a free group, and includes its relative versions. The outer space of a free product is made of $G$-trees with possibly non-trivial vertex stabilisers. The strategies are the same as in the classical case, with some technicalities arising from the presence of infinite-valence vertices. ¶ We describe the Lipschitz metric and show how to compute it; we prove the existence of optimal maps; we describe geodesics represented by folding paths. ¶ We show that train tracks representative...

  12. On a quantum version of Ellis joint continuity theorem

    Das, Biswarup; Mrozinski, Colin
    We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. We give two applications of our results: a “noncommutative” version of Ellis joint continuity theorem for semitopological groups, a corollary to which is a new C∗-algebraic proof of the theorem for classical semitopological semigroup; we also investigate the question of the existence of the Haar state on a compact semitopological quantum semigroup and prove a “noncommutative” version of the converse Haar’s theorem.

  13. Decompositions of rational functions over real and complex numbers and a question about invariant curves

    Müller, Peter
    We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves in the complex plane which are invariant under a rational function.

  14. Holomorphic functional calculus on upper triangular forms in finite von Neumann algebras

    Dykema, K.; Sukochev, F.; Zanin, D.
    The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup–Schultz hyperinvariant projections, behave well with respect to holomorphic functional calculus.

  15. A note on reduced and von Neumann algebraic free wreath products

    Wahl, Jonas
    We study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb{G}\wr_{*}S_{N}^{+}$, where $\mathbb{G}$ is a compact matrix quantum group. Based on recent results on their corepresentation theory by Lemeux and Tarrago in [Lemeux and Tarrago (2014)], we prove that $\mathbb{G}\wr_{*}S_{N}^{+}$ is of Kac type whenever $\mathbb{G}$ is, and that the reduced version of $\mathbb{G}\wr_{*}S_{N}^{+}$ is simple with unique trace state whenever $N\geq8$. Moreover, we prove that the reduced von Neumann algebra of $\mathbb{G}\wr_{*}S_{N}^{+}$ does not have property $\Gamma$.

  16. Model theory and the QWEP conjecture

    Goldbring, Isaac
    We observe that Kirchberg’s QWEP conjecture is equivalent to the statement that $C^{*}(\mathbb{F})$ is elementarily equivalent to a QWEP C$^{*}$ algebra. We also make a few other model-theoretic remarks about WEP and LLP C$^{*}$ algebras.

  17. An isoperimetric inequality for an integral operator on flat tori

    Osting, Braxton; Marzuola, Jeremy; Cherkaev, Elena
    We consider a class of Hilbert–Schmidt integral operators with an isotropic, stationary kernel acting on square integrable functions defined on flat tori. For any fixed kernel which is positive and decreasing, we show that among all unit-volume flat tori, the equilateral torus maximizes the operator norm and the Hilbert–Schmidt norm.

  18. A refinement of analytic characterizations of gaugeability for generalized Feynman–Kac functionals

    Kim, Daehong; Kurniawaty, Mila; Kuwae, Kazuhiro
    We relax the conditions for measures in our previous paper [Analytic characterizations of gaugeability for generalized Feynman–Kac functionals (2016) Preprint] on analytic characterizations of (conditional) gaugeability for generalized Feynman–Kac functionals in the framework of symmetric Markov processes. The analytic characterization is also equivalent to the maximum principle for generalized Feynman–Kac semigroups, extending the result by Takeda [The bottom of the spectrum of time-changed processes and the maximum principle of Schrödinger operators (2015) Preprint].

  19. Compact composition operators with symbol a universal covering map onto a multiply connected domain

    Jones, Matthew M.
    We generalise previous results of the author concerning the compactness of composition operators on the Hardy spaces $H^{p}$, $1\leq p<\infty$, whose symbol is a universal covering map from the unit disk in the complex plane to general finitely connected domains. We demonstrate that the angular derivative criterion for univalent symbols extends to this more general case. We further show that compactness in this setting is equivalent to compactness of the composition operator induced by a univalent mapping onto the interior of the outer boundary component of the multiply connected domain.

  20. Twisted Reidemeister torsion and the Thurston norm: Graph manifolds and finite representations

    Friedl, Stefan; Nagel, Matthias
    We show that the Thurston norm of any irreducible 3-manifold can be detected using twisted Reidemeister torsions corresponding to integral representations and also corresponding to representations over finite fields. In particular, our result holds for all graph manifolds, these are not covered by the earlier work of the first author and Vidussi.

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