A new version of SnapPy, a program for studying the topology and geometry of 3-manifolds, is available. Added features include a census of Platonic manifolds, rigorous computation of cusp translations, and substantial improvements to its link diagram component.

## May 24, 2016

## March 22, 2015

### SnapPy 2.3 released

Marc Culler and I are pleased to announce version 2.3 of SnapPy. New features include:

- Major improvements to the link and planar diagram component, including link simplification, random links, and better documentation.
- Basic support for spun normal surfaces.
- New extra features when used inside of Sage:
- HIKMOT-style rigorous verification of hyperbolic structures,

contributed by Matthias Goerner. - Many basic knot/link invariants, contributed by Robert

Lipschitz and Jennet Dickinson. - Sage-specific functions are now more easily accessible as

methods of Manifold and better documented. - Improved number field recognition, thanks to Matthias.

- HIKMOT-style rigorous verification of hyperbolic structures,
- Better compatibility with OS X Yosemite and Windows 8.1.
- Development changes:
- Major source code reorganization/cleanup.
- Source code repository moved to Bitbucket.
- Python modules now hosted on PyPI, simplifying installation.

All available at the usual place.

## January 5, 2015

### Topology of musical data

A few years ago a musician friend asked me “there’s this new tool topologists have called Persistent Homology. I’d like to see what it can do when you apply it to data from music. Want to help?”

That friend is also an electrical engineer and knows some things about signal processing. This was important to me — we had some external criterion (from outside of mathematics) for determining whether or not the insights from Persistent Homology were interesting or not.

So I said “okay!” Not really knowing what I was getting myself into.

## March 2, 2014

### SnapPy 2.1: Now with extra precision!

Marc Culler and I released SnapPy 2.1 today. The main new feature is the ManifoldHP variant of Manifold which does all floating-point calculations in quad-double precision, which has four times as many significant digits as the ordinary double precision numbers used by Manifold. More precisely, numbers used in ManifoldHP have 212 bits for the mantissa/significand (roughly 63 decimal digits) versus 53 bits with Manifold.

## November 26, 2013

### What’s Next? A conference in question form

Mark your calendars now: in June 2014, Cornell University will host “What’s Next? The mathematical legacy of Bill Thurston”. It looks like it will be a very exciting event, see the (lightly edited) announcement from the organizers below the fold.

## October 13, 2013

### A noteworthy knot simplification algorithm

This post concerns an intriguing undergraduate research project in computer engineering:

Lewin, D., Gan O., Bruckstein A.M.,

TRIVIAL OR KNOT: A SOFTWARE TOOL AND ALGORITHMS FOR KNOT SIMPLIFICATION,

CIS Report No 9605, Technion, IIT, Haifa, 1996.

A curious aspect of the history of low dimensional topology are that it involves several people who started their mathematical life solving problems relating to knots and links, and then went on to become famous for something entirely different. The 2005 Nobel Prize winner in Economics, Robert Aumann, whose game theory course I had the honour to attend as an undergrad, might be the most famous example. In his 1956 PhD thesis, he proved asphericity of alternating knots, and that the Seifert surface is an essential surface which separates alternating knot complements into two components the closures of both of which are handlebodies.

Daniel Lewin is another remarkable individual who started out in knot theory. His topological work is less famous than Aumann’s, and he was murdered at the age of 31 which gives his various achievements less time to have been celebrated; but he was a remarkable individual, and his low dimensional topology work deserves to be much better known. (more…)

## October 2, 2013

### Regina 4.94

It’s the season for it! For those of you who work with normal surfaces, Regina 4.94 also came out last week. It adds triangulated vertex links, edge drilling, and a *lot* more speed and grunt.

Take the new linear/integer programming machinery for a spin with the pre-rolled triangulation of the Weber Seifert dodecahedral space. Regina can now prove 0-efficiency in just 10 seconds, or enumerate all 1751 vertex surfaces in ~10 minutes, or (with a little extra code to coordinate the slicing and searching for compressing discs) prove the entire space to be non-Haken in ~2 hours.

Read more of what’s new, or download and tinker at regina.sourceforge.net.

## September 30, 2013

### SnapPy 2.0 released

Marc Culler and I pleased to announce version 2.0 of SnapPy, a program for studying the topology and geometry of 3-manifolds. Many of the new features are graphical in nature, so we made a new tutorial video to show them off. Highlights include

(more…)

## May 31, 2013

### The algorithm to recognise the 3-sphere

## April 23, 2013

### When are two hyperbolic 3-manifolds homeomorphic?

A preprint of Lins and Lins appeared on the arXiv today, posing a challenge [LL]. In this post, I’m going to discuss that challenge, and describe a recent algorithm of Scott–Short [SS] which may point towards an answer.

**The Lins–Lins challenge**

The theory of 3-manifolds is now very advanced, and we can even say in a certain sense that we understand ‘all’ 3-manifolds (as I discussed in an earlier post). But that understanding is very theoretical; the Lins–Lins challenge is to put this theory into practice.

They ask: ‘Are the two closed, hyperbolic 3-manifolds given by Dehn surgery on the following two framed links homeomorphic?’

(I’ve taken the liberty of copying the diagrams from their paper.)