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Extending the Dehn quandle to shears and foliations on the torus

Reza Chamanara, Jun Hu, Joel Zablow (2014)

Fundamenta Mathematicae

The Dehn quandle, Q, of a surface was defined via the action of Dehn twists about circles on the surface upon other circles. On the torus, 𝕋², we generalize this to show the existence of a quandle Q̂ extending Q and whose elements are measured geodesic foliations. The quandle action in Q̂ is given by applying a shear along such a foliation to another foliation. We extend some results which related Dehn quandle homology to the monodromy of Lefschetz fibrations. We apply certain quandle 2-cycles...

Extension of complexes of groups

André Haefliger (1992)

Annales de l'institut Fourier

Complexes of groups G ( X ) over ordered simplicial complexes X are generalizations to higher dimensions of graphs of groups. We first relate them to complexes of spaces by considering their classifying space B G ( X ) . Then we develop their homological algebra aspects. We define the notions of homology and cohomology of a complex of groups G ( X ) with coefficients in a G ( X ) -module and show the existence of free resolutions. We apply those notions to study extensions of complexes of groups with constant or abelian kernel....

Fatgraph models of RNA structure

Fenix Huang, Christian Reidys, Reza Rezazadegan (2017)

Molecular Based Mathematical Biology

In this review paper we discuss fatgraphs as a conceptual framework for RNA structures. We discuss various notions of coarse-grained RNA structures and relate them to fatgraphs.We motivate and discuss the main intuition behind the fatgraph model and showcase its applicability to canonical as well as noncanonical base pairs. Recent discoveries regarding novel recursions of pseudoknotted (pk) configurations as well as their translation into context-free grammars for pk-structures are discussed. This...

Feuilletages transversalement projectifs sur les variétés de Seifert

Thierry Barbot (2003)

Annales de l’institut Fourier

Soit M une variété de Seifert de groupe fondamental non virtuellement résoluble. Soit Φ un feuilletage de dimension 1 sur M , muni d’une structure projective réelle transverse. On suppose que Φ satisfait la propriété de relèvement des chemins, i.e., que l’espace des feuilles du relèvement de Φ dans le revêtement universel de M est séparé au sens de Hausdorff. On montre qu’à revêtements finis près, Φ est soit une fibration projective, soit un feuilletage géodésique convexe, soit un feuilletage horocyclique...

Fibrations sur le cercle et surfaces complexes

Anne Pichon (2001)

Annales de l’institut Fourier

Nous donnons des conditions nécessaires et suffisantes pour qu’une variété de dimension 3 se réalise comme bord d’une famille dégénérée de courbes complexes, et pour qu’un entrelacs dans une 3-variété se réalise comme bord d’un germe de fonction analytique en un point d’une surface complexe normale. Ces résultats s’appuient sur une étude des objets topologiques fournis par de telles fonctions holomorphes : soit M une variété de Waldhausen et soit L une union finie, éventuellement vide, de fibres...

Fibred closed braids with disc-band fibre surfaces

Marta Rampichini (2004)

Bollettino dell'Unione Matematica Italiana

A classical result by Stallings provides a necessary and sufficient condition to decide whether a given embedded surface S is a fibre in S 3 - ∂ ⁡ S . In this paper it is described how to find a candidate fibre surface for a a link presented as a closed braid. Also it is described an implemented algorithm to find the main ingredients of the necessary and sufficient condition of Stallings, namely presentations of the fundamental groups of the surface and of its complement in S 3 , and an explicit expression of...

Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

We describe the finite group actions, up to equivalence, which can act on the orbifold Σ ( 2 , 2 , 2 ) , and their quotient types. This is then used to consider actions on prism manifolds M ( b , d ) which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If ϕ : G → Homeo ( M ( b , d ) ) is such an action, we show that M ( b , d ) = M ( b , 2 ) and M ( b , 2 ) / ϕ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by Σ ( 2 , 2 , 2 ) . For the standard actions, we compute the fundamental group of M ( b , 2 ) / ϕ and indicate when...

Currently displaying 461 – 480 of 1631