Annals of Mathematics

最新文章

• Integrability of Lie brackets AI翻译
  作者：Crainic, M; Fernandes, RL
  摘要：In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications.
• Axiom A maps are dense in the space of unimodal maps in the Ck topology AI翻译
  作者：Kozlovski, OS
  摘要：In this paper we prove C-k structural stability conjecture for unimodal maps. In other words, we shall prove that Axiom A maps are dense in the space of C-k unimodal maps in the C-k topology. Here k can be 1, 2...., infinity,omega.
• On a coloring conjecture about unit fractions AI翻译
  作者：Croot, ES III
  摘要：We prove an old conjecture of Erdos and Graham on sums of unit fractions: There exists a constant b > 0 such that if we r-color the integers in [2, b(r)], then there exists a monochromatic set S such that Sigma(nis an element ofs) 1/n = 1.
• Norm preserving extensions of holomorphic functions from subvarieties of the bidisk AI翻译
  作者：Agler, J; McCarthy, JE
• A proof of Kirillov's conjecture AI翻译
  作者：Baruch, EM
• Y-systems and generalized associahedra AI翻译
  作者：Fomin, S; Zelevinsky, A
• Knot concordance, Whitney towers and L2-signatures AI翻译
  作者：Cochran, TD; Orr, KE; Teichner, P
  摘要：We construct many examples of nonslice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. The bottom part of the filtration exhibits all classical concordance invariants, including the Casson-Gordon invariants. As a first step, we construct an infinite sequence of new obstructions that vanish on slice knots. These...
• The ionization conjecture in Hartree-Fock theory AI翻译
  作者：Solovej, JP
  摘要：We prove the ionization conjecture within the Hartree-Fock theory of atoms. More precisely, we prove that, if the nuclear charge is allowed to tend to infinity, the maximal negative ionization charge and the ionization energy of atoms nevertheless remain bounded. Moreover, we show that in Hartree-Fock theory the radius of an atom (properly defined) is bounded independently of its nuclear charge.
• On the K-theory of local fields AI翻译
  作者：Hesselholt, L; Madsen, I
• Approximation to real numbers by cubic algebraic integers. II AI翻译
  作者：Roy, D
  摘要：It has been conjectured for some time that, for any integer n greater than or equal to 2, any real number epsilon > 0 and any transcendental real number xi, there would exist infinitely many algebraic integers a of degree at most n with the property that \xi - alpha\ less than or equal to H(alpha)(-n+epsilon), where H(alpha) denotes the height of alpha. Although this is true for n = 2, we show here that, for n = 3, the optimal exponent of approximation is not 3 but (3 + root5)/2 similar or equ...