# How to find Colin Day's PhD Thesis

A week or so ago, I was saddened to read Jim Stasheff's post on the AlgTop mailing list, announcing the passing of Colin Day, after a long bout with cancer.

I was thinking of reading Colin Day's PhD thesis in his memory, and trying to understand it (the title certainly sounds interesting); but I found it to be difficult to access. The reference is:

Day, Colin
A topological construction of Vassiliev style invariants of links.
Thesis (Ph.D.)--The University of North Carolina at Chapel Hill. 1993. 99 pp.

The standard course of action (I think) would be to write to the UNC library and to pay for access; but I'm wondering whether his PhD thesis, or a good summary of it, or anything related is freely available anywhere.

Does anyone know how Colin Day's work can be easily accessed?

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Is he the same person who also has a different(?) dissertation at South Carolina?(genealogy.math.ndsu.nodak.edu/id.php?id=1026) –  Unknown Feb 27 '12 at 9:56
To save others the Googling trouble, here's a link to the UNC library entry: search.lib.unc.edu/search?R=UNCb2492225 -- confusingly, the author they have is Edward Bomback. Unfortunately, they only have print access it seems. –  Thomas Bloom Feb 27 '12 at 10:01
@Unknown: No, it's just a coincidence of names. –  Jim Humphreys Feb 27 '12 at 12:12
@Daniel: Can't you just borrow a paper copy from UNC's library via interlibrary loan? –  Dmitri Pavlov Feb 27 '12 at 16:50
@Jim, an interesting coincidence. –  Unknown Feb 27 '12 at 23:06

I appreciate the interest shown. It apparently is on microfiche. I am in contact with the UNC math library and hope to have access I can share.

Update: It is now available at

http://hans.math.upenn.edu/~jds/

scroll down to Colin...

Please let me know if you access it or if you have trouble accessing it.

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@Jim: I'm shocked and saddened to learn that Colin has passed away! I knew him from several interactions, including a summer at Park City, where I first really got to know him. He was a wonderful guy, and I remember having a conversation with him and Is Singer, and Is saying how very much he had enjoyed meeting Colin. I'm sure that he impressed many people the same way. –  Robert Bryant Feb 27 '12 at 16:59
@jim and Robert. I have the same feelings. I recall him as a lad attending the Georgia topology conference. He was full of enthusiasm and joy of life. –  Scott Carter Feb 27 '12 at 22:47
Excellent! Please forward me a copy (and post a link here), if you get access you can share. Would e-mails from additional people (to show that there is wider interest) help? –  Daniel Moskovich Feb 27 '12 at 23:34
I updated this with the link you posted on ALGTOP-L. Hopefully that is OK. –  Daniel Moskovich Apr 5 '12 at 8:39
Daniel, Thanks for doing that. –  Jim Stasheff Apr 7 '12 at 18:19

It's always worth contacting the dissertation adviser. Aside from that option, dissertations are increasingly available online, typically requiring interlibrary loan services. The company involved is called ProQuest here. Their search form returns this kind of header, followed by a lengthy abstract:

A topological construction of Vassiliev style invariants of links Day, Colin; Stasheff, James D. The University of North Carolina at Chapel Hill, 1993. 1993. 9324015.

To get beyond this public listing, direct purchase or interlibrary loan access then has to be used (which I haven't actually done). Keep in mind that most dissertations don't have lasting scholarly value in themselves. But Colin Day left mathematics soon after his degree and didn't publish further. I hosted his visit to our department when he was considering graduate schools and am saddened to hear of his premature death.

ADDED: Maybe it's useful to quote the online abstract of the thesis (symbols edited).

"An explicit construction of Vassiliev style link invariants is developed; a new construction of Vassiliev knot invariants is shown in the process. Inside the space of all maps $\mathcal{L}_n$ from $\prod_{i=1}^{n} S^1$ to $\mathbb{R}^3$ is the discriminant $\Sigma$, which is the set of maps that are not embeddings. Following Vassiliev, we employ a spectral sequence to find certain homology groups of the discriminant and, using a sort of infinite dimensional Alexander Duality, obtain knot and link invariants which are elements of $\widetilde{H}^0(\mathcal{L}^{n} - \Sigma$) and are link invariants of finite type. To calculate the value of the invariant on a knot or link we need some initial data; the needed data is entered into a table called an actuality table. Following Vassiliev, an inductive algorithm is developed that allows us to trace the progress of a given cycle through the spectral sequence without having to calculate the entire spectra sequence. We carefully investigate the geometry of the discriminant in the course of this development.

"We give examples of how the invariants are derived and how they are evaluated on links. The examples presented include examples of knot invariants, link invariants and invariants of link homotopy; we evaluate one of the invariants of link homotopy for two component links on a whole class of two component links. We also give the generalization to links of Birman and Lin's result that establishes an important relationship between invariants of finite type and a general form of the HOMFLY polynomial."

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