Topic
Mapping torus
About: Mapping torus is a research topic. Over the lifetime, 183 publications have been published within this topic receiving 2293 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, an ideal triangulation of a mapping torus of a pseudo-Anosov map punctured along the singular fibers is constructed, which gives rise to a new conjugacy invariant of mapping classes and a new proof of Farb-Leininger-Margalit.
Abstract: We show how to construct an ideal triangulation of a mapping torus of a pseudo-Anosov map punctured along the singular fibers. This gives rise to a new conjugacy invariant of mapping classes, and a new proof of a theorem of Farb-Leininger-Margalit. The approach in this paper is based on ideas of Hamenstadt.
98 citations
TL;DR: An up-to-date overview of geometric and topological properties of cosymplectic and coKahler manifolds is given in this article, where the authors also mention some of their applications to time-dependent mechanics.
Abstract: We give an up-to-date overview of geometric and topological properties of cosymplectic and coKahler manifolds. We also mention some of their applications to time-dependent mechanics.
86 citations
TL;DR: In this article, the authors studied the minimum dilatation of orientable pseudo-Anosov braid classes coming from fibrations over the circle of a single 3-manifold.
Abstract: In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus g=2,3,4,5,8 as well as Lanneau and Thiffeault's conjectural minima for orientable mapping classes, when g = 2,4 (mod 6). Our examples also show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when g = 4,6,8.
66 citations
TL;DR: In this article, the authors studied the small dilatation pseudo-Anosov mapping classes arising from fibrations over the circle of a single 3-manifold, the mapping torus for the simplest hyperbolic braid.
Abstract: In this paper we study the small dilatation pseudo-Anosov mapping classes arising from fibrations over the circle of a single 3‐manifold, the mapping torus for the “simplest hyperbolic braid”. The dilatations that occur include the minimum dilatations for orientable pseudo-Anosov mapping classes for genus gD2;3;4;5 and 8. We obtain the “Lehmer example” in genus gD 5, and Lanneau and Thiffeault’s conjectural minima in the orientable case for all genus g satisfying gD 2 or 4.mod 6/. Our examples show that the minimum dilatation for orientable mapping classes is strictly greater than the minimum dilatation for non-orientable ones when gD 4;6 or 8. We also prove that if g is the minimum dilatation of pseudo-Anosov mapping classes on a genus g surface, then lim sup g!1 . g/ g 3C p 5
58 citations
TL;DR: In this paper, the authors give an algorithm to compute HF*(f) for a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF_*(h) for h any orientation-preserving mapping class.
Abstract: The symplectic Floer homology HF_*(f) of a symplectomorphism f:S->S encodes data about the fixed points of f using counts of holomorphic cylinders in R x M_f, where M_f is the mapping torus of f. We give an algorithm to compute HF_*(f) for f a surface symplectomorphism in a pseudo-Anosov or reducible mapping class, completing the computation of Seidel's HF_*(h) for h any orientation-preserving mapping class.
55 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 9 |
| 2020 | 10 |
| 2019 | 18 |
| 2018 | 13 |
| 2017 | 11 |
| 2016 | 11 |