I think it would help immensely to get into details and see worked examples. For a complexified algebraic curve, what is the algorithm to construct a detailed tiling of the uniform time domain? (You can use triangularization if you want) By detailed I mean that singular points and algebraic cycles should be marked. To step up a dimension, just ask what happens when the curve/surface depends on a shape parameter. If you start with a genus g=0,1, or 2 surface and deform it continuously via the shape parameter, how can the resulting 3-manifold be described in terms of the Thurston Geometries? So yes, it’s more than I want to know, but also less than what I want to know. For me (and many others), more constructive methods = less confusing formalism. —Brad
On Oct 21, 2020, at 4:08 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Allan Wechsler wrote: ----- I have been trying to wrap my head around this corner of mathematics for my entire adult life, so I will be re-reading this post carefully in hopes of getting some insight.
Unless I missed something, you don't actually define the homology and cohomology groups, do you? You are more saying, "These things exist, but I don't want to get into the details," right? (I think I could reconstruct the definition of the j-th homology group of a simplicial complex, but I'm quite sure I never knew the corresponding definition of the cohomology groups.) -----