Israel Journal of Mathematics最新文献

Let n ≥ 1, and let ({iota _n}:{F_n}(M) to prodnolimits_1^n M ) be the natural inclusion of the n^th configuration space of M in the n-fold Cartesian product of M with itself. In this paper, we study the map ι_n, the homotopy fibre I_n of ι_n and its homotopy groups, and the induced homomorphisms (ι_n)_#k on the k^th homotopy groups of F_n(M) and (prodnolimits_1^n M ) for all k ≥ 1, where M is the 2-sphere ({mathbb{S}^2}) or the real projective plane ℝP².It is well known that the group π_k(I_n) is the homotopy group ({pi _{k + 1}}(prodnolimits_1^n {M,{F_n}} (M))) for all k ≥ 0. If k ≥ 2, we show that the homomorphism (ι_n⁾_#k is injective and diagonal, with the exception of the case n = k = 2 and (M = {mathbb{S}^2}), where it is anti-diagonal. We then show that I_n has the homotopy type of (K({R_{n - 1}},1) times Omega (prodnolimits_1^{n - 1} {{mathbb{S}^2}} )), where R_n−1 is the (n − 1)^th Artin pure braid group if (M = {mathbb{S}^2}), and is the fundamental group G_n−1 of the (n−1)^th orbit configuration space of the open cylinder ({mathbb{S}^2}backslash { {widetilde z_0}, - {widetilde z_0}} ) with respect to the action of the antipodal map of ({mathbb{S}^2}) if M = ℝP², where ({widetilde z_0} in {mathbb{S}^2}). This enables us to describe the long exact sequence in homotopy of the homotopy fibration ({I_n} to {F_n}(M)buildrel {{iota _n}} overlongrightarrow prodnolimits_1^n M ) in geometric terms, and notably the image of the boundary homomorphism ({pi _{k + 1}}(prodnolimits_1^n M ) to {pi _k}({I_n})). From this, if (M = {mathbb{S}^2}) and n ≥ 3 (resp. M = ℝP² and n ≥ 2), we show that Ker((ι_n)_#1 ) is isomorphic to the quotient of R_n−1 by the square of its centre, as well as to an iterated semi-direct product of free groups with the subgroup of order 2 generated by the centre of P_n (M) that is reminiscent of the combing operation for the Artin pure braid groups, as well as decompositions obtained in [GG5].

Let π and τ be irreducible smooth generic representations of SO₅ and GL₂ respectively over a non-archimedean local field. We show that the L- and ε-factors attached to π×π defined by the Rankin–Selberg integrals and the associated Weil–Deligne representation coincide. The proof is obtained by explicating the relation between the Rankin–Selberg integrals for SO₅ × GL₂ and Novodvorsky’s local integrals for GSp₄× GL₂.

An algebra graded by a group G and endowed with a graded involution * is called a (G, *)-algebra. Here we consider G a finite abelian group and classify the subvarieties of the varieties of almost polynomial growth generated by finite-dimensional (G, *)-algebras. Also, we present, up to equivalence, the complete list of (G, *)-algebras generating varieties of at most linear growth. Along the way, we give a new characterization of varieties of polynomial growth generated by finite-dimensional (G, *)-algebras by considering the structure of the generating algebra.

We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion Ĝ of a relatively hyperbolic virtually compact special group G and completely describe finitely generated pro-p subgroups of Ĝ. This applies to the profinite completion of the fundamental group of a hyperbolic arithmetic manifold. We deduce that all finitely generated pro-p subgroups of the congruence kernel of a standard arithmetic lattice of SO(n, 1) are free pro-p.

We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact R-linear functor between R-linear tensor-triangulated categories which are rigidly-compactly generated by their tensor units. We then apply these results to non-positive commutative DG-rings and connective ring spectra. In particular, this gives a support-theoretic classification of (co)localizing subcategories, and thick subcategories of compact objects of the derived category of a non-positive commutative DG-ring with finite amplitude, and provides a formal justification for the principle that the space associated to an eventually coconnective derived scheme is its underlying classical scheme. For a non-positive commutative DG-ring A, we also investigate whether certain finiteness conditions in D(A) (for example, proxy-smallness) can be reduced to questions in the better understood category D(H⁰A).

We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in ℝⁿ, for n ≥ 2, called bounded integrable parameterization mappings, or BIP maps for short. These have the property that the restriction of the Zorich transform to each slice has uniformly bounded derivative in L^n/(n−1). For BIP maps, the logarithmic transform of the mean radius function is bi-Lipschitz. We then apply our result to BIP maps with simple infinitesimal spaces to show that the asymptotic representation is indeed quasiconformal by showing that its Zorich transform is a bi-Lipschitz map.

In this article we extend results of Kakutani, Adler–Flatto, Smilansky and others on the classical α-Kakutani equidistribution result for sequences arising from finite partitions of the interval. In particular, we describe a generalization of the equidistribution result to infinite partitions. In addition, we give discrepancy estimates, extending results of Drmota–Infusino [8].