Among Dennis Johnson’s complete list of works on Celebratio, the reader will find two unpublished preprints:
- “Non-bording diffeomorphisms of surfaces which act trivially on homology” (1978–80) [◊];
- “A geometric version of Casson’s invariant and its application to Reidemeister torsion” (1988) [◊].
We highlight these here as examples of 20th-century mathematical “rarities”: preprints that predate the creation of ArXiv (1992) and so constitute a category of unpublished research that will become difficult for historians to access as mathematicians old enough to have amassed personal libraries of such papers retire and dispose of those materials.
Neither Dennis Johnson nor Klaus Johannson published extensively during their research careers, so “Non-bording diffeomorphisms” is unusual, moreover, as an instance of collaboration. Edmonds and Ewing have suggested [e3] that the preprint was the first time the Jaco–Shalen–Johanson (JSJ) decomposition was applied to questions about surface diffeomorphisms. Priority in such instances can be tricky to establish, however, as Martin Scharlemann underscores in a recent email:1
In fact, before seeing this preprint I had thought my paper [e2] was the first use of JSJ decompositions in studying cobordisms of surface automorphisms. The \( [\dots] \) last paragraph \( [ \)of Johannson–Johnson\( ] \), saying I pointed out an error in their original paper, makes me think that might indeed be true, but it’s hard to tell and really doesn’t matter. In any case, Bonahon then wrote the definitive paper on the subject [e1], inventing “compression-bodies” in the process. Casson must have been involved too, but how exactly I’ve forgotten — and there are no publications.
We note that a concise statement of Johnson and Johannson’s proof of the main result is published, fully credited, in Section 6 of Leininger and Reid’s “The co-rank conjecture for 3-manifold groups” [e5]. The authors further point out that the result was proven independently by Casson (also unpublished, with the citation being a lecture Casson gave at the University of California, Santa Barbara in 1979).2
The second preprint (“A geometric form of Casson’s invariant…”) has proved useful to physicists. Edward Witten characterized it as “unpublished lecture notes” when he cited it for relevant background information in 1991 [e4], and in a recent communication, he reiterated its usefulness for a calculation he recently undertook with Douglas Stanford (see [◊]). Several mathematicians have attested that a typescript version of these notes once existed, but our editors have not been able to locate a copy.
The copy we make available here, in Johnson’s handwriting, is clearly a second- or third-generation photocopy, and we regret that the legibility of the document is poor in places. We make it available nonetheless as a resource for others and in the hopes that a typescript version of the same may yet be found.
– Editors
