組ひも・エントロピー・キャンディーマシーン

2019/06/25 Tue 16:30 - 18:00

6号館809号室

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.