Drew Zemke, who is a grad student of Jason Manning, posted a proof of the Simple Loop Conjecture for 3-manifolds modeled on Sol last week.
The Simple Loop Conjecture fits into that family of statements such as Dehn’s Lemma and the Sphere Theorem which translate statements about fundamental groups into statements about 3-manifolds. Such theorems allow us to trade 3-manifolds for their fundamental groups (which are much simpler mathematical objects). (more…)
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.
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…)
I’ve recently been looking at the following paper in which -TQFT anomalies are treated carefully and various old constructions of Turaev and Walker are elucidated:
Gilmer, P.M. and Masbaum, G., Maslov Index, Mapping Class Groups, and TQFT, Forum Math. 25 (2013), 1067-1106.
It makes me think a lot about just what the anomaly `actually means’… (more…)
Relaxing from my forays into information and computation, I’ve recently been glancing through my mathematical sibling Kenta Okazaki’s thesis, published as:
K. Okazaki, The state sum invariant of 3–manifolds constructed from the linear skein.
Algebraic & Geometric Topology 13 (2013) 3469–3536.
It’s a wonderful piece of diagrammatic algebra, and I’d like to tell you a bit about it! (more…)
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.
Daniel Moskovich recently wrote about the discovery by a lawyer of a duplication in the knot tables called the “Perko pair”.
Now a banker has found another duplicate in yet another table of 3-manifolds. This time it was Ben Burton, and the duplicate appears in the Hildebrand-Weeks cusped hyperbolic census.
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.
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.