Proceedings of the Japan Academy, Series A, Mathematical Sciences

On a structure of random open books and closed braids

Tetsuya Ito

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Abstract

A result of Malyutin shows that a random walk on the mapping class group gives rise to an element whose fractional Dehn twist coefficient is large or small enough. We show that this leads to several properties of random 3-manifolds and links. For example, random closed braids and open books are hyperbolic.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 10 (2015), 160-162.

Dates
First available in Project Euclid: 2 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1449080128

Digital Object Identifier
doi:10.3792/pjaa.91.160

Mathematical Reviews number (MathSciNet)
MR3430206

Zentralblatt MATH identifier
1336.57020

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Random closed braids random open books fractional Dehn twist coefficients quasimorphisms

Citation

Ito, Tetsuya. On a structure of random open books and closed braids. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 10, 160--162. doi:10.3792/pjaa.91.160. https://projecteuclid.org/euclid.pja/1449080128


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