Extending higher dimensional quasi-cocycles

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infinite-dimensional. Our proof is based on an extension to higher degrees of a recent result by Hull and Osin. Namely, we prove that, if H is a hyperbolically embedded subgroup of G and V is any G-module, then any n-quasi cocycle on H with values in V may be extended to G. Also, we show that our extensions detect the geometry of the embedding of hyperbolically embedded subgroups, in a suitable sense.Comment: Minor revisions. This version has been accepted for publication by the Journal of Topolog

Fermion masses in SUSY SO(10) with type II seesaw: a non-minimal predictive scenario

A predictive framework for fermion masses and mixing is given by the supersymmetric SO(10) model with one 10, one bar126, one 126 and one 210 Higgs representations, and type II seesaw dominating the neutrino mass matrix. We investigate the origin of the tension between this model and lepton mixing data and refine previous numerical analyses. We discuss an extension of the minimal model that includes one 120 Higgs chiral superfield representation. This exhausts the possible renormalizable contributions to the Yukawa sector. In spite of the increase in the number of parameters the predictivity of the minimal setting is not spoiled. We argue that the contributions to fermion masses due to the doublet components of 120 can be naturally small compared to those of 10 and 126, thus acting as a perturbation in the fermion mass generation. The antisymmetric nature of the 120 Yukawa coupling affects at leading order the determination of the mixing angles and it allows to remove the inconsistencies between predictions and data on the neutrino parameters. An improvement in the experimental bound on |Ue3| can tell this scenario from the minimal model.Comment: 11 pages, 3 figures; Note and references added on new KamLAND dat

In vivo imaging of the tonoplast intrinsic protein family in Arabidopsis roots

Background: Tonoplast intrinsic proteins (TIPs) are widely used as markers for vacuolar compartments in higher plants. Ten TIP isoforms are encoded by the Arabidopsis genome. For several isoforms, the tissue and cell specific pattern of expression are not known. Results: We generated fluorescent protein fusions to the genomic sequences of all members of the Arabidopsis TIP family whose expression is predicted to occur in root tissues (TIP1;1 and 1;2; TIP2;1, 2;2 and 2;3; TIP4;1) and expressed these fusions, both individually and in selected pairwise combinations, in transgenic Arabidopsis. Analysis by confocal microscopy revealed that TIP distribution varied between different cell layers within the root axis, with extensive co-expression of some TIPs and more restricted expression patterns for other isoforms. TIP isoforms whose expression overlapped appeared to localise to the tonoplast of the central vacuole, vacuolar bulbs and smaller, uncharacterised structures. Conclusion: We have produced a comprehensive atlas of TIP expression in Arabidopsis roots, which reveals novel expression patterns for not previously studied TIPs

Alexander quandle lower bounds for link genera

We denote by Q_F the family of the Alexander quandle structures supported by finite fields. For every k-component oriented link L, every partition P of L into h:=|P| sublinks, and every labelling z of such a partition by the natural numbers z_1,...,z_n, the number of X-colorings of any diagram of (L,z) is a well-defined invariant of (L,P), of the form q^(a_X(L,P,z)+1) for some natural number a_X(L,P,z). Letting X and z vary in Q_F and among the labellings of P, we define a derived invariant A_Q(L,P)=sup a_X(L,P,z). If P_M is such that |P_M|=k, we show that A_Q(L,P_M) is a lower bound for t(L), where t(L) is the tunnel number of L. If P is a "boundary partition" of L and g(L,P) denotes the infimum among the sums of the genera of a system of disjoint Seifert surfaces for the L_j's, then we show that A_Q(L,P) is at most 2g(L,P)+2k-|P|-1. We set A_Q(L):=A_Q(L,P_m), where |P_m|=1. By elaborating on a suitable version of a result by Inoue, we show that when L=K is a knot then A_Q(K) is bounded above by A(K), where A(K) is the breadth of the Alexander polynomial of K. However, for every g we exhibit examples of genus-g knots having the same Alexander polynomial but different quandle invariants A_Q. Moreover, in such examples A_Q provides sharp lower bounds for the genera of the knots. On the other hand, A_Q(L) can give better lower bounds on the genus than A(L), when L has at least two components. We show that in order to compute A_Q(L) it is enough to consider only colorings with respect to the constant labelling z=1. In the case when L=K is a knot, if either A_Q(K)=A(K) or A_Q(K) provides a sharp lower bound for the knot genus, or if A_Q(K)=1, then A_Q(K) can be realized by means of the proper subfamily of quandles X=(F_p,*), where p varies among the odd prime numbers.Comment: 36 pages; 16 figure

Integral Foliated Simplicial Volume of Aspherical Manifolds

We consider the relation between simplicial volume and two of its variants: the stable integral simplicial volume and the integral foliated simplicial volume. The definition of the latter depends on a choice of a measure preserving action of the fundamental group on a probability space. We show that integral foliated simplicial volume is monotone with respect to weak containment of measure preserving actions and yields upper bounds on (integral) homology growth. Using ergodic theory we prove that simplicial volume, integral foliated simplicial volume and stable integral simplicial volume coincide for closed hyperbolic 3-manifolds and closed aspherical manifolds with amenable residually finite fundamental group (being equal to zero in the latter case). However, we show that integral foliated simplicial volume and the classical simplicial volume do not coincide for hyperbolic manifolds of dimension at least 4

A constant dark matter halo surface density in galaxies

We confirm and extend the recent finding that the central surface density r_0*rho_0 galaxy dark matter halos, where r_0 and rho_0 are the halo core radius and central density, is nearly constant and independent of galaxy luminosity. Based on the co-added rotation curves of about 1000 spiral galaxies, mass models of individual dwarf irregular and spiral galaxies of late and early types with high-quality rotation curves and, galaxy-galaxy weak lensing signals from a sample of spiral and elliptical galaxies, we find that log(r_0*rho_0) = 2.15 +- 0.2, in units of log(Msol/pc^2). We also show that the observed kinematics of Local Group dwarf spheroidal galaxies are consistent with this value. Our results are obtained for galactic systems spanning over 14 magnitudes, belonging to different Hubble Types, and whose mass profiles have been determined by several independent methods. In the same objects, the approximate constancy of rho_0*r_0 is in sharp contrast to the systematical variations, by several orders of magnitude, of galaxy properties, including rho_0 and central stellar surface density.Comment: Accepted for publication in MNRAS. 9 pages, 4 figure