筑波大学トポロジーセミナー

# 世話人：川村一宏，平山至大，石井敦，丹下基生，蓮井翔

日時 | ２０１３年１０月３１日（木）１６：００－１７：３０ |
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場所 | 筑波大学 自然系学系Ｄ棟 Ｄ５０９ |

講演者 | 金英子 氏 （大阪大学 理学研究科） |

講演題目 | Pseudo-Anosovs with small dilatations coming from the magic 3-manifold |

アブストラクト | Pseudo-Anosov mapping classes are equipped with some constants >1 called the dilatation. It is known that the logarithm of the dilatation is exactly equal to the topological entropy of a pseudo-Anosov representative of its mapping class. By work of Thurston, if a hyperbolic fibered 3-manifold M has the second Betti number more than 1, then it admits infinitely many fibrations on M. Moreover the monodromy of any fibration on M is pseudo-Anosov. As an example of such manifolds, we consider a single 3-manifold N with 3 cusps called the magic 3-manifold. We compute the dilatation of monodromy of each fibration on N. We also discuss the problem on the minimal dilatations and their asymptotic behavior. Intriguingly, pseudo-Anosovs with the smallest known dilatations are ``coming from" the magic 3-manifold. This is a joint work with Mitsuhiko Takasawa. |

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