Welcome to MathOverflow

Question

6

Floer's paper, An Instanton-Invariant for 3-Manifolds, makes reference to Casson's construction of a topological invariant for homology 3-spheres. He literally references it by placing the bibliographic-tag [C] in one of his sentences... but he doesn't actually list it in the bibliography!
I subsequently search around, and cannot find where Casson originally defines his invariant; only locate papers that talk about his invariant. Does this "paper" not exist? I would think that such an important construction has a foundational paper in existence.

flag	asked Oct 5 at 23:03 Chris Gerig 5,526●1●12●40

3

This seems like the kind of question that at least half of the Berkeley math department would know the answer to instantaneously. If you Google "Casson Invariant" you get endless papers. – Ryan Budney Oct 6 at 3:04

Benjamin Dickman · Accepted Answer · 2012-10-08 16:38:10Z UTC

9

According to the following paper, this invariant's introduction is sourced as: A. Casson, Lecture notes, MSRI Lectures, Berkeley, 1985.

The first published discussion appears to be found in: S. Akbulut & J. McCarthy, Casson's invariant for oriented homology 3-spheres, an exposition, Math. Notes, No. 36, Princeton Univ. Press, Princeton, 1990.

"I don't know if he [Casson] has ever written his notes. I attended his lectures at MSRI then I went back to MSU and tried to fill in the details together with McCarthy, those notes are the result." S. Akbulut

"Here is a pdf of hand-written notes of T. Cochran's. Page two includes annotated notes by Boyer, and I got the notes from my friend and colleague, A. Nicas." H. Boden

edited Oct 8 at 16:38

answered Oct 5 at 23:28

Benjamin Dickman
1,869●1●6●21

In 1990 there are a number of papers on Casson's invariant, most notably Kevin Walker's Bulletin announcement of his extension, so I don't think Akbulut-McCarthy is the first published version. – Igor Rivin Oct 6 at 0:50

1

I mean in terms of expository work around the introduced invariant; that said, I've emailed Akbulut and MSRI to see if they are aware of digitalized lecture notes that are accessible. I'll update if/when I receive a response. – Benjamin Dickman Oct 6 at 0:58

2

I haven't thought about this stuff for a long time, but I think Akbulut and McCarthy is the standard reference for Casson's original construction. I don't recall ever seeing any polished notes coming directly from Casson's lectures, so I doubt any such notes were ever digitized. – Kevin Walker Oct 6 at 4:14

2

The notes of Cochran's that you link to look familiar, so I think they must have been the notes I had in the 1980's. I had long ago lost my copy and forgotten who took the notes, so thanks for locating these. – Kevin Walker Oct 8 at 20:17

Seeking a seemingly missing reference of Casson

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.