Found! (very probably…)

I think I’ve found the mysterious author of the notes on 3-manifolds: it is (or should be) G. P. Scott. The crucial clue is the fact that the notes claim that the author, and Shalen independently, proved that “3-manifold groups are coherent”, and then gives the proof. This would immediately clarify things, were it not for the fact that (1) Shalen never published his proof; (2) the terminology “coherent” doesn’t seem to be really well known for groups, really. What it is defined to mean is the following: a group G is coherent if and only if, all its finitely generated subgroups are finitely presented.

But, as it happens, even Scott’s paper proving this doesn’t seem to use the terminology! (In MathSciNet, there are ten papers by someone named Scott including “coherent” somewhere in the review — but again that one is not among them) Fortunately, Google did find some references for “Shalen coherent”, in particular a Bourbaki seminar by J. Stallings reporting on Scott’s result (which gives, in particular, simple examples of non-coherent groups).

[Note: On Scott’s page, I found what seems to be a quite nice survey of The geometries of 3-manifolds, from 1983.]

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Kowalski

I am a professor of mathematics at ETH Zürich since 2008.