It is true that I am reading a paper of J. Milnor's from 1956 or so, but only part of it [1]; more accurately, I'm reading enough of it to determine whether a certain property of spheres [2] is false in the C1-smooth setting; it is known to be false in the C∞-smooth setting.
On that note, it's actually been a bit of fun. I'm reviewing some differential topology that I hadn't thought about in ages, and am finally applying some facts that I thought would be useful only for passing my Topology qual.
- I've struck upon a regular bit of confusion, though: perhaps I'm bad with the notation, but it doesn't seem easy to tell where a particular function is 'living' (i.e. its domain, and whether I am looking in the chart or on the manifold ..). Hence the title.
- Of course, the fun might end soon. There's a sizable section or two which requires some knowledge of homology and cohomology. As you can imagine, algebraic topology isn't my strong point .. \:
Oh well. Que sera, sera, and it's back to work for me!
[1] In particular, it's "On Manifolds Homeomorphic to the 7-Sphere" from the Sept 1956 Annals of Mathematics.
[2] and yes, I am deliberately being vague. q:
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