Why I’m not a topologist

Yes, I’m still alive. This quarter my favorite class is on knot theory. In particular, we are studying Khovanov homology. The point of Khovanov homology is to give a stronger knot invariant than the Jones polynomial which also has nice categorical (functorial) properties. The Jones polynomial can then be recovered from the Khovanov complex by taking the alternating sum of the ranks of the homology, in the same way that the Euler characteristic can be recovered from normal (simplicial/singular/whatever) homology. Today the professor mentioned that he found drawing knot diagrams to compute the Khovanov complex fun because when he was a student people told him that he should understand chain complexes and homological algebra, but he preferred pretty pictures since he’s a topologist. So I looked at the knot diagrams and the algebraic chain complexes and decided I prefer the chain complexes. I guess I’m not meant to be a topologist.


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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6 Responses to Why I’m not a topologist

  1. mad_emperor says:

    Hey, hows math?
    I guess I won’t be able to go to the seminar on Tuesdays cuz I won’t have time. I’m already doing an independent project with Prof. Agboola on Number Theory. But mann, this guy is scarry! He will never be satisfied with my work.

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