Đề tài " The Tits alternative for Out(Fn) II: A Kolchin type theorem " pot

... ·····[f k−1 (u i )] Annals of Mathematics The Tits alternative for Out(Fn) II: A Kolchin type theorem By Mladen Bestvina, Mark Feighn, and Michael Handel THE TITS ALTERNATIVE FOR Out(F n ) II 19 for ... lemma to { A k } we learn that for all large k there is a lift A  k of A k that terminates at y. For infinitely many k, A  k starts at...

Ngày tải lên: 22/03/2014, 20:20

... of certain ‘sums-of-squares’ formulas over a field F, related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of charac- teristic ... . Proposition A. 3 shows that the left vertical map is an isomorphism. Lemma A. 9 identifies the right vertical map as the diagonal, and from that information the result fo...

Ngày tải lên: 06/03/2014, 08:21

... Johnson). Introduction Let A be a Banach algebra, E an A- bimodule. A linear mapping D : A E is called a derivation,ifD(ab)=aD(b)+D (a) b for all a, b A ([D, Def. 1.8.1]). For x ∈ E, we define the inner derivation ad x : ... the proof of Lemma 4.2. Remark 4.3. (a) There are numerous examples of transformation groups that admit a quasi-invariant probability measure but no...

Ngày tải lên: 06/03/2014, 08:21

... where the special intervals are located after the related F i ’s. For example it shows that there is a gap between F i and the first special interval of the form I i,s (if any) that is at least ... E 1 contradicting Lemma 5 The proof for the other cases is similar. The assertion (ii) follows again by Lemma 5, (iii) can be proved in a similar way as (i) and (iv) can be pro...

Ngày tải lên: 14/03/2014, 22:20

... series are indexed by the singular cusps {a} and are given by: E a (z,s)=  γ∈Γ a \Γ χ(γ)j σ −1 a γ (z) −k (m(σ −1 a γz)) s where σ a is a scaling matrix for the cusp a. Recall that the scaling matrix ... amplified mean square over a well chosen family. Before doing so we need to transform slightly these sums. The reason for these apparently unmotivated transformati...

Ngày tải lên: 22/03/2014, 16:20

... θ, and fix also ε to be a sufficiently small positive number, and η to be a positive number sufficiently small in the context of Theorems 3 and 4 and the associated auxiliary mean value estimates, and ... no suitable reference available in the literature. However, the argument that we apply is nonetheless largely standard, and so we shall be brief. First we introduce the approximants...

Ngày tải lên: 22/03/2014, 20:21

... Using the same definitions as for the ordinary case gives a Selmer mod- ule that is not a torsion Iwasawa module [Ru1], and a p-adic L-function that does not belong to the Iwasawa algebra [MTT], [AV]. ... torsion Iwasawa modules. It then follows from (1) and (c) that U/C and X have the same characteristic ideal, and from (b) that the characteristic ideal of U/C is a (“two-v...

Ngày tải lên: 28/03/2014, 22:20

... denoted A. Let A ∗ and A be fixed once and for all. By compactness, there exists r 0 > 0 such that for each x ∈ M, there exists i(x) such that the Riemannian ball of radius r 0 around x is contained ... cru- cial to the proofs of Theorems 1 through 4. It captures the idea of sequence of linear transformations that can be (almost) realized on subsets with large relative measur...

Ngày tải lên: 06/03/2014, 08:21

... apologise for the complexity of the 252 NIKOLAY NIKOLOV AND DAN SEGAL argument. The basic idea in all cases is the same: the required result is reduced to showing that certain equations are solvable ... A 2 and i = 2, the set ω(i) \ ω(i + 1) contains a single root v. Then Y i = X v (aF 0 ) · Y i+1 , where a = 1 for type A 1 , and a ∈ F is any solution of a + a...

Ngày tải lên: 29/03/2014, 07:20