Braids and entropies from taffy pulling machines

Date
2019/06/25 Tue 16:30 - 18:00
Room
6号館809号室
Speaker
Dr. Eiko Kin
Affiliation
Osaka University
Abstract

Taffy pullers are devices for pulling candy.
One can build braids from the motion of rods for taffy pullers.
According to the article ``A mathematical history of taffy pullers" by Jean-Luc Thiffeault,
all taffy pullers (except the first one) give rise to pseudo-Anosov braids.
This means that the devices mix candies effectively.

Braids are classified in three categories, periodic, reducible and pseudo-Anosov.
The last category is the most important one for the study of dynamical systems.
Each pseudo-Anosov braid determines its stretch fact and the logarithm of stretch factor is called the entropy.
Following a study of Thiffeault, I discuss which pseudo-Anosov braids are realized by taffy pullers, and how to compute their entropies.
I explain an interesting connection between braids coming from taffy pullers and hyperbolic links.
Interestingly, the two most common taffy pullers give rise to the complements of the the minimally twisted 4-chain link and 5-chain link which are important examples for the study of cusped hyperbolic 3-manifolds with small volumes.
If time permits, I will explain a construction of pseudo-Anosov braids.