A note on semi-conjugacy for circle actions

We define a notion of semi-conjugacy between orientation-preserving actions of a group on the circle, which for fixed point free actions coincides with a classical definition of Ghys. We then show that two circle actions are semi-conjugate if and only if they have the same bounded Euler class. This settles some existing confusion present in the literature

QuasiI-State Rigidity for Finite-Dimensional Lie Algebras

We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C-n x u( n), n = 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimensio

Kac–Moody symmetric spaces

In the present article we introduce and study a class of topological reflectionspaces that we call Kac–Moody symmetric spaces. These are associated with split realKac–Moody groups and generalize Riemannian symmetric spaces of noncompact split type.Based on work by the third-named author, we observe that in a non-spherical Kac–Moody symmetric space there exist pairs of points that do notlie on a common geodesic;however, any two points can be connected by a chain of geodesic segments. We moreoverclassify maximal flats in Kac–Moody symmetric spaces and study their intersection patterns,leading to a classification of global and local automorphisms. Some of our methods apply togeneral topological reflection spaces beyond the Kac–Moodysetting.Unlike Riemannian symmetric spaces, non-spherical non-affine irreducible Kac–Moodysymmetric spaces also admit an invariant causal structure.For causal and anti-causal geo-desic rays with respect to this structure we find a notion of asymptoticity, which allows usto define a future and past boundary of such Kac–Moody symmetric space. We show thatthese boundaries carry a natural polyhedral cell structureand are cellularly isomorphic togeometric realizations of the two halves of the twin buildings of the underlying split real Kac–Moody group. We also show that every automorphism of the symmetric space is uniquelydetermined by the induced cellular automorphism of the future and past boundary.The invariant causal structure on a non-spherical non-affineirreducible Kac–Moody sym-metric space gives rise to an invariant pre-order on the underlying space, and thus toa subsemigroup of the Kac–Moody group.We conclude that while in some aspects Kac–Moody symmetric spaces closely resembleRiemannian symmetric spaces, in other aspects they behave similarly tomasures, their non-Archimedean cousin

Defective HSV-1 vector expressing BDNF in auditory ganglia elicits neurite outgrowth: model for treatment of neuron loss following cochlear degeneration

The neurotrophins are a family of growth factors that play an important role in the development and maintenance of the nervous system. Brain-derived neurotrophic factor (BDNF) is a member of the neurotrophin family that appears to participate in the maturation and function of mammalian auditory neurons. Forms of deafness due to varied injurious stimuli that are amenable to treatment with implantable prosthetic devices require the survival of these BDNF-responsive auditory neurons for effective outcome. To evaluate the feasibility of developing a gene therapy for deafness that may be used in conjunction with a prosthetic device, we constructed replication-defective herpes simplex virus (HSV) amplicon vectors that carry the human BDNF cDNA. Using these vectors, HSVbdnf and HSVbdnflac (expresses BDNF and Escherichia coli beta-galactosidase), we evaluated the expression and biological activity in established cell lines and explant cultures prepared from spiral ganglia of the murine ear. Gene transfer with HSVbdnf resulted in the efficient expression of human BDNF mRNA in murine fibroblasts. Using two BDNF-responsive cell lines, PC12trkB and MG87trkB, we demonstrate efficient secretion of biologically active BDNF. Finally, transduction of explanted spiral ganglia with HSVbdnflac elicited robust neuritic process outgrowth comparable to exogenously added BDNF. Overall, these data demonstrate that HSV vectors can efficiently transfer and express the BDNF gene in many cell types, including auditory neurons. Moreover, they suggest that similar vectors may be used to express the neurotrophin in auditory neurons in vivo and perhaps as adjunctive gene therapy for deafness

NT-3 combined with CNTF promotes survival of neurons in modiolus-spiral ganglion explants.

Auditory neurons depend upon the integrity of both their peripheral (auditory hair cells) and central (cochlear nucleus) targets for survival. One proposed trophic mechanism is the production of neurotrophin-3 (NT-3) by auditory hair cells. Modiolus-spiral ganglion explants from adult rats that closely mirror cell-cell interactions and in vivo tissue relationships within this ganglion provide a model for testing trophic factors. Brain derived neurotrophic factor (BDNF), NT-3 and ciliary neurotrophic factor (CNTF) were tested for their ability, both individually and in combination, to support neuronal survival. NT-3 was the strongest individual promoter of survival, while CNTF (a cytokine) with NT-3 (a neurotrophin) was the most effective combination for promoting the survival of auditory neurons