Low Dimensional Topology

May 29, 2008

Reidemeister’s stabilization paper

Filed under: 3-manifolds,Heegaard splittings — Jesse Johnson @ 2:41 pm

The idea of stabilizing Heegaard splittings (which I’ve mentioned quite a few times) was discovered independently by Kurt Reidemeister and James Singer, each of whom published a paper about it in 1933. Singer’s paper was published in Transactions of the AMS and can be found on JSTOR. Reidemeister’s paper, on the other hand, appeared in a more obscure journal, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. This journal is so obscure that MathSciNet only lists its contents back to 1987, a good 54 years after Reidemeister’s paper. (I didn’t realize there were gaps in MathSciNet, but surprise!)

Needless to say, the contents from the 1933 issue aren’t available on line. However, it turns out Yale has the journal going back to the very first issue. Since stabilization is rather important to me, I though I’d scan in the paper. I then discovered I could run it through optical character recognition software to turn the ugly scanned PDFs into a fairly nice .tex file, which I then cleaned up and fixed the math symbols. The final product looks pretty nice (though it’s still in German). If you want to see which typos are original and which were introduced by me, you can also download the original scans. I know this probably violates the paper’s copyright, but I hope whoever owns the copyright won’t mind.

Also, while I’m at it, here’s a link to Waldhausen’s paper (also in German) on classifying Heegaard splittings of the 3-sphere. If you don’t want to learn German, you can get a good idea of the proof by reading this paper by Loretta Bartolini and Hyam Rubinstein, which uses a very similar proof to classify one sided Heegaard splittings of RP^3.  Or (as Andy Putman has pointed out) you can read Saul Schleimer’s account of Waldhausen’s proof.

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4 Comments »

  1. Another (english language) source for Waldhausen’s proof of Waldhausen’s theorem is a recent paper of Saul Schleimer :
    http://www.msp.warwick.ac.uk/gtm/2007/12/p012.xhtml

    Comment by Andy P. — May 29, 2008 @ 6:54 pm | Reply

  2. Thanks. I didn’t know about that paper.

    Comment by Jesse Johnson — May 29, 2008 @ 7:08 pm | Reply

  3. Very nice. Have you considered feeding the OCR’ed text to one of the online translators?

    Comment by saul — May 31, 2008 @ 5:49 am | Reply

  4. I have tried online translators and it’s pretty funny. Here’s an HTML version of the text so you can try it yourself. I think WorldLingo, Microsoft Live and Abacho did relatively readable jobs.

    Comment by Jesse Johnson — May 31, 2008 @ 7:49 am | Reply


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