Volume 24, Issue 5

Abstract. Let N be a finitely generated normal subgroup of a Gromov hyperbolic group . We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of . We show that the hyperbolic group from F. Haglund's and D. Wise's version of Rips's construction is hereditarily conjugacy separable. We then use this construction to produce first examples of finitely generated and finitely presented conjugacy separable groups that contain non-(conjugacy separable) subgroups of finite index.

Abstract. The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group and the closed manifold subgroup are equal in dimensions , for any finitely-presented group and any orientation character . This answers a question raised in 1980.

Abstract. In this paper we establish the self-improving property of integrability for parabolic variational inequalities satisfying an obstacle constraint and involving possibly degenerate respectively singular operators in divergence form. In particular, our results apply to the model case of the variational inequality associated to the parabolic p -Laplacean operator. Thereby we do not impose any monotonicity assumption in time on the obstacle function.

Abstract. We adapt Levi's parametrix method to construct local fundamental solutions for operators of the form , where are Hörmander vector fields of step 2 having non-smooth coefficients. We also provide estimates of and of its derivatives.

Abstract. The Kuykian conjecture for a Hilbertian field K says that if is an abelian variety, then every intermediate field of is Hilbertian. We prove the Kuykian conjecture in the following cases: (a)  K  is finitely generated (over its prime field). (b)  for almost all , where F is a finitely generated field. (c) , where F is the quotient field of a complete local domain of dimension at least 2.

Abstract. Manifold calculus of functors, due to M. Weiss, studies contravariant functors from the poset of open subsets of a smooth manifold to topological spaces. We introduce “multivariable” manifold calculus of functors which is a generalization of this theory to functors whose domain is a product of categories of open sets. We construct multivariable Taylor approximations to such functors, classify multivariable homogeneous functors, apply this classification to compute the derivatives of a functor, and show what this gives for the space of link maps. We also relate Taylor approximations in single variable calculus to our multivariable ones.

Abstract. Taking a weighted version of Bini–Meini–Poloni symmetrization procedure for a multivariable geometric mean, we propose a definition for a weighted geometric mean of n positive definite matrices, where the weights vary over all n -dimensional positive probability vectors. We show that the weighted mean satisfies multidimensional versions of all properties that one would expect for a two-variable weighted geometric mean. Significant portions of the derivation can be and are carried out in general convex metric spaces, which means that the results have broader application than the setting of positive definite matrices.

Abstract. Kaplansky classes emerged in the context of Enochs' solution of the Flat Cover Conjecture. Their connection to abstract model theory goes back to Baldwin et al.: a class of roots of Ext is a Kaplansky class closed under direct limits if and only if the pair is an abstract elementary class (AEC) in the sense of Shelah. We prove that this AEC has finite character in case for a class of pure-injective modules. In particular, all AECs of roots of Ext over any right noetherian right hereditary ring R have finite character (but the case of general rings remains open). If is an AEC of roots of Ext, then is known to be a covering class. However, Kaplansky classes need not even be precovering in general: We prove that the class of all ℵ 1 -projective modules (which is equal to the class of all flat Mittag-Leffler modules) is a Kaplansky class for any ring R , but it fails to be precovering in case R is not right perfect, the class equals the class of all flat modules and consists of modules of projective dimension . Assuming the Singular Cardinal Hypothesis, we prove that is not precovering for each countable non-right perfect ring R .