Low Dimensional Topology

February 5, 2013

Wise’s CBMS Lecture Notes on Cube Complexes

Filed under: 3-manifolds,Hyperbolic geometry,Virtual Haken Conjecture — Jesse Johnson @ 2:39 pm

This fall, the topology group at OSU is reading through Dani Wise’s lecture notes on cube complexes, based on his series of talks at the CBMS-NSF conference back in 2011.  Henry Wilton and Daniel Moskovich have written on this blog about Wise’s work and its role in the proof of the Virtual Haken Conjecture. This is just a quick note to say how  impressed I’ve been with the lecture notes. They start from the very beginning, include a lot of good examples and have proved to be very accessible for all of us non-experts (which includes me).

It’s just too bad that Wise’s notes are no longer available on the conference web page. (Now that a paper copy is available from the AMS, the PDF file has been replaced with a note saying that the editor insisted they be taken down.)  You can still e-mail Dani Wise to request a copy, but I expect that some people (such as beginning graduate students) might be reluctant to e-mail someone they don’t know like this. I can assure you, he was very gracious when I asked him for a copy and seems to be very eager to distribute the notes widely. But, if you have any thoughts on how the PDF file could be distributed more efficiently, I would love to hear about it in the comments.

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November 10, 2012

SnapPy 1.7: Ptolemy and reps to PSL(n, C).

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry,Triangulations — Nathan Dunfield @ 2:45 pm

SnapPy 1.7 is out. The main new feature is the ptolemy module for studying representations into PSL(n, C). This code was contributed by Mattias Görner, and is based on the the following two very interesting papers:

  1. Stavros Garoufalidis, Matthias Goerner, Christian K. Zickert: Gluing equations for PGL(n,C)-representations of 3-manifolds.
  2. Stavros Garoufalidis, Dylan P. Thurston, Christian K. Zickert: The complex volume of SL(n,C)-representations of 3-manifolds.

You can get the latest version of SnapPy at the usual place.

September 8, 2012

ICERM Fall 2013: Topology, geometry, and dynamics

I’ve mentioned before that the fall semester program at ICERM for 2013 will focus on computation in low-dimensional topology, geometry, and dynamics.   You can now apply to be a long-term visitor for this as a graduate student, postdoc, or other.   The deadline for the postdoctoral positions is January 14, 2013; the early deadline for everyone else is December 1, 2012 and the second deadline March 15, 2013.

There will also be three week-long workshops associated with this, so mark your calendars for these exciting events:

  1. Exotic Geometric Structures. September 15-20, 2013.
  2. Topology, Geometry, and Group Theory: Informed by Experiment. October 21-25, 2013.
  3. Geometric Structures in Low-Dimensional Dynamics. November 18-22, 2013.

August 22, 2012

Bill Thurston is dead at age 65.

Bill Thurston passed away yesterday at 8pm, succumbing to the cancer that he had been battling for the past two years.   I don’t think it’s possible to overstate the revolutionary impact that he had on the study of geometry and topology.  Almost everything we blog about here has the imprint of his amazing mathematics.    Bill was always very generous with his ideas, and his presence in the community will be horribly missed.    Perhaps I will have something more coherent to say later, but for now here are some links to remember him by:

August 1, 2012

SnapPy 1.6: Now with more links and precision!

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry,Knot theory — Nathan Dunfield @ 8:37 am

Marc Culler and I have released version 1.6 of SnapPy.  There are two sets of new features:

  1. Creating links formulaically, e.g. via combining tangles algebraically.  See our page of examples.
  2. Arbitrary precision calculation of certain things (e.g. tetrahedra shapes) and finding associated number fields, a la Snap.   Very basic at this point compared to what Snap can to, but here are examples of what we have so far.  To use this, you need to install SnapPy in Sage, which should be easy.

April 13, 2012

The virtual Haken conjecture

Agol’s preprint, which includes a long appendix joint with Groves and Manning, is now on the arXiv.

March 27, 2012

Agol’s work on the Virtual Haken Conjecture

Over at Geometry and the Imagination, Danny Calegari is reporting live from Paris on talks by Agol and Manning on the announced proof of the VHC:  Part I, Part II, Part III

February 20, 2012

New SnapPy 1.5, now with better manifolds

Filed under: 3-manifolds,Computation and experiment,Hyperbolic geometry,Triangulations — Nathan Dunfield @ 12:47 pm

Marc Culler and I have released version 1.5 of SnapPy, which you can get from the usual place. The main new feature is greatly improved manifold censuses, including the ability check if a given manifold is in one; here are many examples of now to use the new censuses.

I never blogged about version 1.4, since while there were major changes they were mostly under the hood, principally moving to the current version of IPython and making snappy (mostly) compatible with Python 3.2.

November 11, 2011

Who cares about the Volume Conjecture?

Filed under: Hyperbolic geometry,Knot theory,Quantum topology — dmoskovich @ 9:49 am

Yesterday, I attended a very interesting informal talk by Roland van der Veen in which, among other things, he told me a little bit about why he cares about the Volume Conjecture. The Volume Conjecture is considered somehow to be the `big open problem’ in quantum topology. I had never understood why though (I had even asked an MO question but hadn’t really been convinced by any of the very good answers). Why, after all, should people care about any mathematical conjecture? (more…)

November 1, 2011

Videos for NSF-CBMS Cubulationathon

I’ve mentioned here several times the work of Wise on residual properties of certain word-hyperbolic groups, specifically those of Haken hyperbolic 3-manifolds. You can now view all 10 of Dani’s talks at the NSF-CBMS conference (as well as all the other talks) at the conference webpage. The picture and audio quality is quite reasonable considering the setup that was used, and they are certainly watchable.

I really wish more conferences did this. While it’s certainly true that the benefits of attending a conference go far beyond the content of the talks themselves, I think it’s still quite valuable to have this online for those who weren’t able to addend.

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