Tài liệu Đề tài " Dynamics of SL2(R) over moduli space in genus two " ppt

... O K 1 ×···×O K n . Annals of Mathematics Dynamics of SL2(R) over moduli space in genus two By Curtis T. McMullen* DYNAMICS OF SL 2 ( R ) OVER MODULI SPACE IN GENUS TWO 415 equipped with ... By passing to a covering space of E if necessary, we can assume p ∗ (H 1 (X, Z)) = H 1 (E,Z); then the degree of ω is the degree of p. DYNAMICS OF...

Ngày tải lên: 16/02/2014, 06:20

... equivalent to that of the corresponding tensor. This is the key initial point of this article, allowing us to use in Section 1 the results in [G-S1] in order to construct the moduli space of g  -sheaves, ... of E i . After fixing the Chern classes of E and of the line bundles associated to the principal bundle P and characters of G, we obtain a projective moduli spa...

Ngày tải lên: 16/02/2014, 05:20

... −1 11  ;  0 s  j . 4.12 Lemma.Γ k is of finite index in SL(2, ) ( 1 2 ) 2k . Proof. The subgroup Γ θ 2k ⊂ Γ k is of finite index in SL(2, ) 2k and thus also in SL(2, ) ( 1 2 ) 2k . 434 JENS MARKLOF 4.13. Remark. Note ... Theorem 1.4 in [27] on the equidistribution of translates of unipotent orbits. Because of the simple structure of the Lie groups studied here, the proof...

Ngày tải lên: 14/02/2014, 16:20

... ranks of the quotients of the lower central series of π 1 of certain arrangements, in combinatorial terms. The LCS formula for pure braid groups was discovered by Kohno, starting from his pioneering ... H  passing through the origin. Moreover, in this case, the polar curve Γ H ,being defined by homogeneous equations, is a union of lines L j passing through the origin. For each s...

Ngày tải lên: 14/02/2014, 16:20

... Therefore we conclude in this case that the conjugate of the surface S  belongs to the irreducible subset of the moduli space containing S. We are now going to explain the construction of our examples: Let ... structure. Proof. Observe that since S is a classifying space for the fundamental group of π 1 (S), then by the isotropic subspace theorem of [Cat3] the Albanese mapp...

Ngày tải lên: 14/02/2014, 16:20

... . 4. Joint continuity in the · 2 -norm There is an extensive literature on the topic of joint and separate con- tinuity of functions of two variables (see [3], [28] and the references therein) with ... y)isjointly continuous at (b, 0), and thus at (0,0) from above. Since φ(x, y)=ψ(xu ∗ ,y), joint continuity of φ at (0,0) follows immediately. We now show joint continuity at a gen...

Ngày tải lên: 14/02/2014, 17:20

... 1. Density of primitive lattice points. The main obstacle in our approach to finding lowerbounds on Hausdorff dimension is the absence of primitive lattice points in certain regions of the plane. ... smallest closed interval containing all the limits obtainable by applying Lemma 2.3 to a sequence beginning with w. Define E(λ):=∩E j where E j is the union of the intervals associated t...

Ngày tải lên: 14/02/2014, 17:20

... proof is a straightforward adaptation and generalization of the proof of Proposition 3 in [3]. We outline the main steps, while skipping the details. Step 1. One of the basic ingredients in the ... obtain dN/η copies of S η,N : S j η,N ,j=1, , dN η ,(2.43) and each point of R d is contained in exactly d copies. 2. We are going to look at how often the two Brownian motions cr...

Ngày tải lên: 14/02/2014, 17:20

... point stabilizers in GL 2 (Z) × GL 3 (Z) × GL 3 (Z) of the elements in the space of 2 × 3 × 3 integer matrices. Just as stabilizers in GL 2 (Z) of integer points in the space of binary quadratic ... determine the stabilizers over Z of the other two spaces of forms indicated above, again in terms of the unit groups of orders in cubic fields. This article is o...

Ngày tải lên: 14/02/2014, 17:20

... Z d . 5. Proofs of main results Proof of Theorem 1.1. Denote m =  d−1 4 . By applying Corollary 3.4 to m + 1 independent copies of the USF relation, and invoking Theorems 4.2 and 4.5, we infer that ... in E 1 and delet- ing the edges in E 2 . Let H be the graph obtained from Z d by contracting the edges in K 1 and deleting the edges in K 2 . By first choosing Υ  R and continui...

Ngày tải lên: 14/02/2014, 17:20