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All about the place I see this is ’to appear’ in Adv. Math. clearly it hasn’t. What’s the deal? Is this (up to equivalence) the material that is on Todd’s private web?
David and David –
As often seems to happen with me and David C., my usual computer experiences some malfunction just before he wants my attention to something, and it takes a while for me to get up and going on this other computer, and particularly to get around to comments which have piled up and which are invisible on the front page.
The deal is that I seem to be unable to reach Margaret McIntyre, who works in Ghana. Theoretically it seems possible to send email to her department (they have some sort of internet access), but I lack any sort of direct line to her, and I have no idea whether she has read the emails I’ve sent. So that paper “to appear” does seem to be in some kind of limbo.
What is on my personal web is at a more advanced stage of thinking than where M & T ever got in official collaboration, but is obviously woefully incomplete. The issue is made worse by the fact that I really don’t know how to draw pictures in any sort of graphic package, and I seem to have trouble in any sort of sporadic attempt to learn how. The whole thing makes me a little sad.
David R.: are you interested in this?
Todd - yes. (to clarify, it is the sort of interest that mathematicians suffer from: ’ooh, that looks interesting, I had to a calculation that looked like that once’. And we know where that ends up ;-)
But more seriously, I came across similar constructions when trying to talk about homotopy group(oid)s of topological groupoids (hence topological stacks): I needed to talk about surface diagrams in object spaces where the edges were decorated with arrows (i.e. paths in the object space). In the end I gave up on the general case, and restricted to rectilinear diagrams.
And if it helps, I have a little skill in drawing pictures in graphic packages.
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