Finite groups acting on 3-manifolds and cyclic branched coverings of knots

We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point set. This condition is satisfied by the isometry group of any hyperbolic cyclic branched covering of a strongly invertible knot as well as by the isometry group of any hyperbolic 2-fold branched covering of a knot in the 3-sphere. In the paper we give a characterization of nonsolvable groups of this type. Then we consider some possible applications to the study of cyclic branched coverings of knots and of hyperelliptic diffeomorphisms of 3-manifolds. In particular we analyze the basic case of two distinct knots with the same cyclic branched covering.Comment: This is the version published by Geometry & Topology Monographs on 29 April 200

Fibered spherical 3-orbifolds

In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3-orbifolds were described by Dunbar. In this paper we deal with the fibered case and in particular we give explicit formulae relating the finite subgroups of $\mathrm{SO}(4)$ with the invariants of the corresponding fibered 3-orbifolds. This allows to deduce directly from the algebraic classification topological properties of spherical 3-orbifolds.Comment: 27 pages, 6 figures. Several misprint corrected, improved expositio

On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups

It is known that the order of a finite group of diffeomorphisms of a 3-dimensional handlebody of genus g > 1 is bounded by the linear polynomial 12(g-1), and that the order of a finite group of diffeomorphisms of a 4-dimensional handlebody (or equivalently, of its boundary 3-manifold), faithful on the fundamental group, is bounded by a quadratic polynomial in g (but not by a linear one). In the present paper we prove a generalization for handlebodies of arbitrary dimension d, uniformizing handlebodies by Schottky groups and considering finite groups of isometries of such handlebodies. We prove that the order of a finite group of isometries of a handlebody of dimension d acting faithfully on the fundamental group is bounded by a polynomial of degree d/2 in g if d is even, and of degree (d+1)/2 if d is odd, and that the degree d/2 for even d is best possible. This implies then analogous polynomial Jordan-type bounds for arbitrary finite groups of isometries of handlebodies (since a handlebody of dimension d > 3 admits S^1-actions, there does not exist an upper bound for the order of the group itself ).Comment: 13 pages; this is the final version to appear in Fund. Mat

On finite simple and nonsolvable groups acting on closed 4-manifolds

We show that the only finite nonabelian simple groups which admit a locally linear, homologically trivial action on a closed simply connected 4-manifold $M$ (or on a 4-manifold with trivial first homology) are the alternating groups $A_5$, $A_6$ and the linear fractional group PSL(2,7) (we note that for homologically nontrivial actions all finite groups occur). The situation depends strongly on the second Betti number $b_2(M)$ of $M$ and has been known before if $b_2(M)$ is different from two, so the main new result of the paper concerns the case $b_2(M)=2$. We prove that the only simple group that occurs in this case is $A_5$, and then give a short list of finite nonsolvable groups which contains all candidates for actions of such groups.Comment: 17 page

On finite groups acting on acyclic low-dimensional manifolds

We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogue remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting a smooth action on an acyclic 5-manifold are the alternating groups A_5 and A_6, and deduce from this a short list of finite groups, closely related to the finite subgroups of SO(5), which are the candidates for orientation-preserving actions on acyclic 5-manifolds.Comment: 15 pages; improved versio

Hyperbolic 2-fold Branched Coverings

In the Kirby list is presented the following problem: describe the equivalence classes in the set of knots under the relation K$_{1}$ is equivalent to K$_{2}$ if their 2-fold cyclic branched coverings are homeomorphic 3-manifolds. In this paper we consider the basic case of hyperbolic manifold. In the fi{}rst part of this paper we want to present briefl{}y the results, yet available in some previous works, which solve this problem. In the second part we present examples of knots with the same 2-fold branched covering which show that the theorem, which describes the possible relations between two knots in the same equivalence class, is the best possible

MicroRNA MIR396 regulates the switch between stem cells and transit-amplifying cells in arabidopsis roots

To ensure an adequate organ mass, the daughters of stem cells progress through a transit-amplifying phase displaying rapid cell division cycles before differentiating. Here, we show that Arabidopsis thaliana microRNA miR396 regulates the transition of root stem cells into transit-amplifying cells by interacting with GROWTH-REGULATING FACTORs (GRFs). The GRFs are expressed in transit-amplifying cells but are excluded from the stem cells through inhibition by miR396. Inactivation of the GRFs increases the meristem size and induces periclinal formative divisions in transit-amplifying cells. The GRFs repress PLETHORA (PLT) genes, regulating their spatial expression gradient. Conversely, PLT activates MIR396 in the stem cells to repress the GRFs. We identified a pathway regulated by GRF transcription factors that represses stem cell-promoting genes in actively proliferating cells, which is essential for the progression of the cell cycle and the orientation of the cell division plane. If unchecked, the expression of the GRFs in the stem cell niche suppresses formative cell divisions and distorts the organization of the quiescent center. We propose that the interactions identified here between miR396 and GRF and PLT transcription factors are necessary to establish the boundary between the stem cell niche and the transit-amplifying region.Fil: Rodriguez Virasoro, Ramiro Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; ArgentinaFil: Ercoli, María Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; ArgentinaFil: Debernardi, Juan Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; ArgentinaFil: Breakfield, Natalie W.. University of Duke; Estados UnidosFil: Mecchia, Martin Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; ArgentinaFil: Sabatini, Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; ArgentinaFil: Cools, Toon. University of Ghent; BélgicaFil: De Veylder, Lieven. University of Ghent; BélgicaFil: Benfey, Philip N.. University of Duke; Estados UnidosFil: Palatnik, Javier Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Biología Molecular y Celular de Rosario. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Biología Molecular y Celular de Rosario; Argentin