- my crackpot ideas (for reviving the dead thesis problem back into life) aren't working. that should come as no surprise, of course, but these days i can't help but take such things personally ..
- .. which can't possibly be healthy. then again, how healthy can it be, to think about mathematics for most of the day? q:
- so, after having thought a little about group actions in the contexts of the conformally-natural extension of circle homeomorphisms (cf Douady and Earle) and the hyperbolic tiling extension (cf Kirby, Siebenmann, Sullivan), i think i'm entitled to this opinion:
- i hate group-equivariant mappings, at least when it comes to second derivatives.
you'd think that actions by isometries would be reasonably nice, but no. there is an inherent problem between equivariance via group conjugations F = g F g-1 (which are, heuristically speaking, rescalings of space) and second derivatives (which are quantities describing curvature).
meanwhile, the metric co-tangent bundle theory does look interesting .. if that's what it's called.
between the work of N. Weaver and that of J. Cheeger, there are function algebras and abstract constructions running amok and amidst the analysis on metric spaces and measure-theoretic geometry. it feels like i'm walking around a space station and gawking at the various alien races, all the while asking myself,
"what am i supposed to be doing, here?"
and somehow, i suppose that when i answer that question, i'll know what my thesis problem is.
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