And in truth, the picture in S.2.2 on page 14 could be construed as "Lazy". Compare with this 3/4 drawing: https://0x0.st/zgkO.png . --Brad On Wed, Nov 6, 2019 at 4:52 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Mis-spelling both "Hausdorff" and "Euclidean" in the first paragraph of chapter 1 portends an alarming lack of proofreading ... WFL
On 11/6/19, Brad Klee <bradklee@gmail.com> wrote:
These notes from IPhT are starting to look nice, especially with color figures: https://arxiv.org/pdf/1805.06405.pdf , and middle of page 16 mentions the realization that everyone needs to have about genus zero: "(it has the topology of a cylinder)". Shouldn't this be more than an after-thought? It is another way of saying "both sinh(t) and cosh(t) are singly-periodic functions over the complex plane". This analogy between surface topology and periodicity of parametric functions extends to higher genus, and begets the grand "Riemann Uniformization Theorem".
My personal issue, today's gripe, is with Theorem 3.5 "Genus zero = Riemann sphere". This theorem is copied from place to place in just about every reference on algebraic topology. Such practice excludes that "Genus zero = Harmonic Hyperboloid", arguably a more fundamentally correct statement. Students continue to go unaware, while the same mantra gets over-used, again and again. I feel like I have already complained about this, repeatedly.
This whole thing about the Riemann Sphere being the one True Form of Genus Zero (TFGZ) has become too dogmatic for me. I'm planning to release more detailed Heresy in the near future, so watch out!
Cheers
--Brad
PS. For more info about "Harmonic Hyperboloid", see also:
https://demonstrations.wolfram.com/SemiclassicalApproximationForQuantumHarmo...
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