Mathematics papers 2

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30p kienkim1980 19-11-2015 32 2   Download

The goal of this paper is to describe all closed, aspherical Riemannian manifolds M whose universal covers M have a nontrivial amount of symmetry. By this we mean that Isom(M ) is not discrete. By the well-known theorem of Myers-Steenrod [MS], this condition is equivalent to [Isom(M ) : π1 (M )] = ∞. Also note that if any cover of M has a nondiscrete isometry group, then so does its universal cover M . Our description of such M is given in Theorem 1.2 below. The proof of this theorem uses methods from Lie theory, harmonic maps,...

27p dontetvui 17-01-2013 54 7   Download

This paper is about a class of strange attractors that have the dual property of occurring naturally and being amenable to analysis. Roughly speaking, a rank one attractor is an attractor that has some instability in one direction and strong contraction in m−1 directions, m here being the dimension of the phase space. The results of this paper can be summarized as follows. Among all maps with rank one attractors, we identify, inductively, subsets Gn, n = 1, 2, 3, · · · ,

133p dontetvui 17-01-2013 46 6   Download

It is well known that not every orientation-preserving homeomorphism of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is “almost” a welding in a precise way. The proofs are based on Koebe’s circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings. 1. Introduction Let D ⊂ R2 be the open unit disk, let D∗ = S 2 \D and let T = ∂D = ∂D∗ be the unit circle. ...

45p dontetvui 17-01-2013 49 8   Download

The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

28p noel_noel 17-01-2013 52 6   Download

Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. M¨nzner showed that the four principal curvatures can u have at most two distinct multiplicities m1 , m2 , and Stolz showed that the pair (m1 , m2 ) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isoparametric hypersurface of FKM-type, constructed by Ferus, Karcher and M¨nzner from orthogonal representations of Clifford algebras. In this paper, u we prove that if the multiplicities satisfy m2 ≥ 2m1 − 1, then the isoparametric hypersurface M must be...

77p noel_noel 17-01-2013 47 7   Download

Annals of Mathematics By Curtis T. McMullen* .Annals of Mathematics, 165 (2007), 397–456 Dynamics of SL2(R) over moduli space in genus two By Curtis T. McMullen* Abstract This paper classifies orbit closures and invariant measures for the natural action of SL2 (R) on ΩM2 , the bundle of holomorphic 1-forms over the moduli space of Riemann surfaces of genus two. Contents 1. Introduction 2. Dynamics and Lie groups 3. Riemann surfaces and holomorphic 1-forms 4. Abelian varieties with real multiplication 5. Recognizing eigenforms 6. Algebraic sums of 1-forms 7. Connected sums of 1-forms 8.

61p noel_noel 17-01-2013 58 6   Download

Let Γ be a principal congruence subgroup of SLn (Z) and let σ be an Γ irreducible unitary representation of SO(n). Let Ncus (λ, σ) be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for Γ which transform under SO(n) according to σ. In this paper we Γ prove that the counting function Ncus (λ, σ) satisfies Weyl’s law. Especially, this implies that there exist infinitely many cusp forms for the full modular group SLn (Z). Contents 1. Preliminaries 2. Heat kernel estimates 3. Estimations of the discrete spectrum 4....

60p noel_noel 17-01-2013 59 7   Download

In this paper we extend M. Lyubich’s recent results on the global hyperbolicity of renormalization of quadratic-like germs to the space of C r unimodal maps with quadratic critical point. We show that in this space the boundedtype limit sets of the renormalization operator have an invariant hyperbolic structure provided r ≥ 2 + α with α close to one.

95p noel_noel 17-01-2013 52 6   Download

The purpose of this paper is to carry out the abelianization program proposed by Atiyah [1] and Hitchin [9] for the geometric quantization of SU(2) Wess-Zumino-Witten model. Let C be a Riemann surface of genus g. Let Mg be the moduli space of semi-stable rank 2 holomorphic vector bundles on C with trivial determinant. For a positive integer k, let Γ(Mg , Lk ) be the space of holomorphic sections of the k-th tensor product of the determinant line bundle L on Mg . An element of Γ(Mg , Lk ) is called a rank 2 theta function...

50p noel_noel 17-01-2013 64 8   Download

Let p be a prime number, F a totally real field such that [F (µp ) : F ] = 2 and [F : Q] is odd. For δ ∈ F × , let [ δ ] denote its class in F × /F ×p . In this paper, we show Main Theorem. There are infinitely many classes [ δ ] ∈ F × /F ×p such that the twisted affine Fermat curves Wδ : have no F -rational points. Remark. It is clear that if [ δ ] = [ δ ], then Wδ is isomorphic to Wδ over F . For any δ ∈ F × , Wδ /F has rational points locally everywhere.

25p noel_noel 17-01-2013 43 6   Download

This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramification locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert fibred). As a corollary, any smooth orientationpreserving nonfree finite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic definitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with fixed points 2.4.

97p noel_noel 17-01-2013 49 6   Download

This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .

77p noel_noel 17-01-2013 71 5   Download

For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the fluctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, namely that their distribution is that of a certain weighted sum of traces of independent matrices in SU(2).

20p noel_noel 17-01-2013 62 6   Download

This article concludes the comprehensive study started in [Sz5], where the first nontrivial isospectral pairs of metrics are constructed on balls and spheres. These investigations incorporate four different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extensions. In [Sz5] the considerations are completely concluded in the ball-case and in the nilpotent-case. The other cases were mostly outlined. In this paper the isospectrality theorems are completely established on spheres. ...

54p noel_noel 17-01-2013 56 5   Download

This is the second of two papers in which we prove the Tits alternative for Out(Fn ). Contents 1. Introduction and outline 2. Fn -trees 2.1. Real trees 2.2. Real Fn -trees 2.3. Very small trees 2.4. Spaces of real Fn -trees 2.5. Bounded cancellation constants 2.6. Real graphs 2.7. Models and normal forms for simplicial Fn -trees 2.8. Free factor systems 3. Unipotent polynomially growing outer automorphisms 3.1. Unipotent linear maps 3.2. Topological representatives 3.3. Relative train tracks and automorphisms of polynomial growth 3.4. Unipotent representatives and UPG automorphisms ...

60p noel_noel 17-01-2013 46 5   Download

Invariant measures for the geodesic flow on the unit tangent bundle of a negatively curved Riemannian manifold are a basic and well-studied subject. This paper continues an investigation into a 2-dimensional analog of this flow for a 3-manifold N . Namely, the article discusses 2-dimensional surfaces immersed into N whose product of principal curvature equals a constant k between 0 and 1, surfaces which are called k-surfaces.

37p noel_noel 17-01-2013 45 5   Download

This paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed 3manifold. The key is to understand the structure of an embedded minimal disk in a ball in R3 . This was undertaken in [CM3], [CM4] and the global version of it will be completed here; see the discussion around Figure 12 for the local case and [CM15] for some more details. Our main results are Theorem 0.1 (the lamination theorem) and Theorem 0.2 (the one-sided curvature estimate). ...

44p tuanloccuoi 04-01-2013 64 7   Download

In 1970 Alexander Grothendieck [6] posed the following problem: let Γ1 and Γ2 be finitely presented, residually finite groups, and let u : Γ1 → Γ2 be a ˆ homomorphism such that the induced map of profinite completions u : Γ1 → Γ2 ˆ ˆ is an isomorphism; does it follow that u is an isomorphism? In this paper we settle this problem by exhibiting pairs of groups u : P → Γ such that Γ is a direct product of two residually finite, hyperbolic groups, P is a finitely presented subgroup of infinite index, P is not...

16p tuanloccuoi 04-01-2013 52 5   Download

Annals of Mathematics In our first article [2] we developed a new view of Gauss composition of binary quadratic forms which led to several new laws of composition on various other spaces of forms. Moreover, we showed that the groups arising from these composition laws were closely related to the class groups of orders in quadratic number fields, while the spaces underlying those composition laws were closely related to certain exceptional Lie groups.

23p tuanloccuoi 04-01-2013 64 7   Download