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:

Klein Bottle000

Picture 9

Picture 5

Picture 26


The 3-sphere as two balls

Picture 14

Trefoil with monodromy sweep ghostedTrefoil with monodromy annulusTrefoild with mondoromy sweep 2

Trefoil with monodromy annulus 2


Picture 47

Medial surface of the Whitehead link.

StandardContactStructure4 (by epsilon_is_afraid_of_zeta)




Photo 8

ctctstr4, originally uploaded by epsilon_is_afraid_of_zeta.



conformal supports


hopf band monodromy

Picture 7

Picture 6

Ko's Octahedral relation-2

7_7-Sutured Manifold Decomp


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.
2 with 5 copies origview

Here they have order 3.
3 with 4 copies origview

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.
1 with 5 copies origview

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.

Triangulation I, II, III, IV






Whitehead flythrough


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.


About isomorphismes

Argonaut: someone engaged in a dangerous but potentially rewarding adventure.
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