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We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of Kn(Z[G])⊗Z Q...

Three themes are treated in the results announced here. The first is the regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is the geometric convergence of a (sub)sequence of manifolds with boundary with such geometrical bounds and a...

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity conditions expressed in terms of Jacobian matrices and determinants. In the context of chemical reaction networks with power-law kinetics, our results can be used t...

Classes of objects injective w.r.t. specified morphisms are known to be closed under products and retracts. We prove the converse: a class of objects in a locally presentable category is an injectivity class iff it is closed under products and retracts. This result requires a certain large-cardinal principle. We characterize classes of objects injective w.r.t. a small collection of morphisms: t...

Consider a sequence of pointed n–dimensional complete Riemannian manifolds {(Mi, gi(t), Oi)} such that t ∈ [0, T ] are solutions to the Ricci flow and gi(t) have uniformly bounded curvatures and derivatives of curvatures. Richard Hamilton showed that if the initial injectivity radii are uniformly bounded below then there is a subsequence which converges to an n–dimensional solution to the Ricci...

In this paper we study the local and global injectivity of spatial deformations of shearable nonlinearly elastic rods. We adopt an analytical condition introduced by Ciarlet & Ne cas in nonlinear elasticity to ensure global injectivity in that case. In particular we verify the existence of an energy minimizing equilibrium state without self-penetration which may be also restricted by a rigid ob...

Continuous lattices were characterised by Mart́ın Escardó as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω →֒ ω + 1 and 0 →֒ 1. For every class H of morphisms we study the subcategory of all objects Kan-in...

Branner-Hubbard motion is a systematic way of deforming an attracting holomorphic dynamical system f into a family (fs)s∈L, via a holomorphic motion which is also a group action. We establish the analytic dependence of fs on s (a result first stated by Lyubich) and the injectivity of fs on f . We prove that the stabilizer of f (in terms of s) is either the full group L (rigidity), or a discrete...