Low Dimensional Topology

January 5, 2009

Well written topology papers?

Filed under: Misc. — Jesse Johnson @ 7:29 pm

I’m at the Joint Meetings in DC this week, so rather a long post, I thought I would ask a question:  Which research papers (preferably, but not necessarily, in topology) do you think of as examples/models of well written papers?  I’ve always thought that Scharlemann and Thompson’s paper Thin position for 3-manifolds is both well paced and clearly written, to the extent that each step in their reasoning seems almost trivial.   But I’m obviously biased.  What papers do you wish that others would use as models when they write?


  1. Stallings’ “Whitehead graphs on handlebodies.”

    Comment by Richard Kent — January 5, 2009 @ 9:21 pm | Reply

  2. oh, and, see you bright and early tomorrow!

    Comment by Richard Kent — January 5, 2009 @ 9:22 pm | Reply

  3. McMullen’s “From dynamics on surfaces to rational points on curves”.

    Comment by Andy P. — January 5, 2009 @ 9:42 pm | Reply

  4. I like “Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds”
    by Nathan Dunfield. I was thinking once that there should be a website with user generated Amazon.com-style ratings for math papers. I noticed recently that Zentralblatt allows one to leave comments, so at least you could let the world know about your favorite papers.

    Comment by Ian Agol — January 6, 2009 @ 1:35 pm | Reply

  5. For me, Curt McMullen and Marc Lackenby consistently write exceptionally clear and well-organized papers, the kind you can just sit down and read through. As for specific models, I’ll go with Curt’s “The Alexander polynomial of a 3-manifold and the Thurston norm on cohomology” and Marc’s “Covering spaces of 3-orbifolds”.

    Comment by Nathan Dunfield — January 6, 2009 @ 4:56 pm | Reply

  6. I’m assuming that I can’t vote for myself this time. So I’ll go with a favorite paper from grad school — Peter Scott’s “The geometries of $3$-manifolds” was amazingly easy to read and at the same time amazingly instructive. His paper “There are no fake Seifert fibre spaces with infinite pi_1” was also fun, as I recall.

    Comment by Saul Schleimer — January 6, 2009 @ 7:49 pm | Reply

  7. Marc Lackenby’s “Dehn Surgery on Knots in 3-manifolds” is a model for how to write a paper which uses the inner workings of very technical machinery.

    Scott and Tucker’s paper on exotic non-compact 3-manifolds (I don’t recall the title) contains beautiful examples and is enjoyable reading.

    Comment by Scott Taylor — January 7, 2009 @ 7:33 am | Reply

  8. On a more elementary topic, I’ve vote for Mary Ellen Rudin’s “unshellable 3-ball” paper:

    An unshellable triangulation of a tetrahedron, Bull. Am. Math. Soc. (64), 1958, pp.~90–91.

    Of course it is very short.

    Here is another:

    W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds. Ann. of Math. (2) 76 (1962), 531–540.

    This is fairly easy to read.

    Comment by blueollie — January 12, 2009 @ 12:05 pm | Reply

  9. if i recall correctly, the *only* math paper
    (in its original journal publication
    and *not* written by me) i *ever* read for pleasure
    was something of john milnor‘s.
    but that would’ve been in the early 90s
    & today i can’t even tell you its title.
    also i saw him lecture once. he’s good at that too.

    Comment by vlorbik — January 22, 2009 @ 1:07 pm | Reply

  10. no, dammit. it was something of richard *swan*’s.
    *cited* by milnor, i imagine somehow … probably
    _characteristic_classes_. and *he’s* the guy
    whose talk i admired, too. okay. my mind is going.
    gee this is embarrassing. feel free to delete these.

    Comment by vlorbik — January 23, 2009 @ 4:45 pm | Reply

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