If you don’t read Sketches of Low-Dimensional Topology already, your personal astrologer advises that you start doing so before the next ecliptic.
Sample pics and text:
ctctstr4, originally uploaded by epsilon_is_afraid_of_zeta.
View this 3-manifold as an interval of concentric spheres where you have to imagine gluing the inner sphere to the outer sphere.
Near each point on a singular fiber, a regular fiber passes by some fixed number of times, the order of the singular fiber. In the picture above this number is 5 for both singular fibers.
Here they have order 2.
Here they have order 3.
Here they have order 1 and so they aren’t that special. A homeomorphism would make all the fibers appear as radial arcs, the S^1‘s of the S^1 x S^2.
For the conference honoring the 60th birthday ofCaroline Series(only a German wiki?!?), I was one of a handful asked to contribute pictures inspired by her work. First up is my contribution followed by a description. After that are a few more.
I don’t think I will ever be this awesome. Not only are the pictures way easier to understand than some scary symbols, but the text explains their meaning really clearly and in not-too-many words.
Pass the acid—I mean, the advanced mathematics—please. People thought Grigory Perelman was crazy for turning down a million-dollar prize and living like an ascetic. “Why should I jump for a million dollars, when I can control the vacuum space in between the quarks of the universe?” is my paraphrase of his reply. I don’t have a million dollars, nor do I understand all of this ring fiber link knot book page contact braid surgery stuff. But right now I’m honestly not sure which I would prefer: the imagination, or the dinero.
Thanks to Maxime (@2_43112609_1 on twitter) for the pointer.
