Related papers: Distinctness of two pseudo-Anosov maps

We give a characterization of generic pseudo-Anosov mapping classes purely in terms of their expressions in the shear coordinates, thus giving an answer to a problem raised by Papadopoulos--Penner [PP93]. This characterization has a cluster…

In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic…

We prove a classification theorem for transitive Anosov and pseudo-Anosov flows on closed 3-manifolds, up to orbit equivalence. In many cases, flows on a 3-manifold $M$ are completely determined by the set of free homotopy classes of their…

We show that one can find two nonisomorphic curves over a field K that become isomorphic to one another over two finite extensions of K whose degrees over K are coprime to one another. More specifically, let K_0 be an arbitrary prime field…

For a pseudo-Anosov homeomorphism $f$ on a closed surface of genus $g\geq 2$, for which the entropy is on the order $\frac{1}{g}$ (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded,…

We construct differential models for degree-3 twisted $\mathrm{Spin}^c$-bordism and for its Anderson dual. The model for the differential Anderson dual is based on the framework of Yamashita--Yonekura. Using these differential models, we…

Let $g\colon L\rightarrow L$ be an atoroidal, endperiodic map on an infinite type surface $L$ with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, $g$ is isotopic to a spun…

Starting from any pseudo-Anosov map $\varphi$ on a surface of genus $g \geqslant 2$, we construct explicitly a family of Derived from pseudo-Anosov maps $f$ by adapting the construction of Smale's Derived from Anosov maps on the two-torus.…

A pseudo-Anosov flow is said to have perfect fits if there are stable and unstable leaves that are asymptotic in the universal cover. We give an algorithm to decide, given a box decomposition of a pseudo-Anosov flow, if the flow has perfect…

This paper describes a family of pseudo-Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g+1 strands determines a hyperelliptic…

An infinite family of generalized pseudo-Anosov homeomorphisms of the sphere S is constructed, and their invariant foliations and singular orbits are described explicitly by means of generalized train tracks. The complex strucure induced by…

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a…

We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong pinching, C^{1+\beta} smoothness of the…

We analyze the rel leaves of the Arnoux-Yoccoz translation surfaces. We show that for any genus $g \geq 3$, the leaf is dense in the connected component of the stratum $H(g -1 , g -1)$ to which it belongs, and the one-sided imaginary-rel…

We show that finitely generated, purely pseudo-Anosov subgroups of the fundamental groups of surface bundles over tori are convex cocompact as subgroups of the mapping class group via the Birman exact sequence. This generalizes the fact…

We present a metric version of weak proper discontinuity (WPD) for pseudo-Anosov maps on surfaces. As an application, we show that there are plenty of quasi-morphisms on the homeomorphism group of a torus or a hyperbolic surface that are…

We investigate the structure of the characteristic polynomial det(xI-T) of a transition matrix T that is associated to a train track representative of a pseudo-Anosov map [F] acting on a surface. As a result we obtain three new polynomial…

For a fixed marked surface $S$, we construct polynomial bounds on the periodic and preperiodic lengths of the maximal splitting sequences of a projectively invariant measured train track. We give two consequences of these bounds. Firstly,…

An $n$-vertex graph is degree 3-critical if it has $2n - 2$ edges and no proper induced subgraph with minimum degree at least 3. In 1988, Erd\H{o}s, Faudree, Gy\'arf\'as, and Schelp asked whether one can always find cycles of all short…

The work that consists of two parts is devoted to the problem of enumerating unrooted $r$-regular maps on the torus up to all its symmetries. We begin with enumerating near-$r$-regular rooted maps on the torus, projective plane and the…