Low Dimensional Topology

December 19, 2017

Computation in geometric topology

Complete lecture videos for last week’s workshop Computation in Geometric Topology at Warwick are now posted on YouTube. The complete list of talks with abstracts and video links is here.

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May 24, 2016

SnapPy 2.4 released

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry,Knot theory — Nathan Dunfield @ 6:11 pm

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.

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:
  • 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.

March 9, 2015

Complex hyperbolic geometry of knot complements

Filed under: 3-manifolds,Hyperbolic geometry,Misc. — dmoskovich @ 3:41 am

This morning there was a paper which caught my eye:

Deraux, M. & Falbel, E. 2015 Complex hyperbolic geometry of the figure-eight knot.
Geometry & Topology 19, 237–293.

In it, the authors study a very different geometric structure for the figure-eight knot complement, as the manifold at infinity of a complex hyperbolic orbifold. (more…)

March 2, 2014

SnapPy 2.1: Now with extra precision!

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry,Knot theory — Nathan Dunfield @ 11:39 pm

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.

(more…)

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.

Conference banner
(more…)

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…)

April 23, 2013

When are two hyperbolic 3-manifolds homeomorphic?

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry — Henry Wilton @ 7:46 am

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?’

Lins-Lins manifolds

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

(more…)

April 20, 2013

The next big thing in quantum topology?

Filed under: 3-manifolds,Hyperbolic geometry,Quantum topology,Triangulations — dmoskovich @ 11:02 pm

The place to be in May for a quantum topologist is Vietnam. After some wonderful-sounding mini-courses in Hanoi, the party with move to Nha Trang (dream place to visit) for a quantum topology conference.

I’d like to tell you very briefly about some exciting developments which I expect will be at the centre of the Nha Trang conference, and which I expect may significantly effect the landscape in quantum topology. The preprint in question is 1-Efficient triangulations and the index of a cusped hyperbolic 3-manifold by Garoufalidis, Hodgson, Rubinstein, and Segerman (with a list of authors like that, you know it’s got to be good!). (more…)

April 6, 2013

New connection between geometric and quantum realms

Filed under: Hyperbolic geometry,Knot theory,Quantum topology — dmoskovich @ 9:41 am

A paper by Thomas Fiedler has just appeared on arXiv, describing a new link between geometric and quantum topology of knots. http://arxiv.org/abs/1304.0970

This is big news!! (more…)

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