/sci/ - Science & Math

>>11403631
>0 function isn't differentiable

>>9735741
>>9735799
See Atiyah - Geometry and Physics of Knots. It's a great read and will prepare you for TQFT.

>>9736955
>Maybe to you even sets are an obscure formalism
They are and most Mathematical Physicists would agree with me on this. Sets are a clunky way of describing our world, a world which is inherently invariant under physical equivalence, while sets are not. Physicists of the older generation are more likely to reject fancy mathematical constructs, but I'm sure this is about to change. So sets are merely seen as an obscure formalism with no real physical meaning backing it. You can sit around and compare large cardinals all day, but that would have no empirical meaning and so we choose to disregard such activities. I would suggest you do the same if you care about pesky little things like meaning and coherence.
>What are you even going on?
I am talking about the community of people who have dedicated their lives to studying TQFT, i.e. Mathematical Physicists. And I am talking about people who advocate for inane formalism and notation usually being unable to even draw a picture of a cofibration or a weak equivalence. Which just shows how the unnecessary abstraction has a tendency to limit creative and spatial thinking which is so inherent to human beings. Surely even you and other "mathematicians" must see that as a negative. It's never too late to develop your physical intuitions so I see no reason for this kind of behavior from you guys.
>Pic related.
I'm not stupid enough to believe that the homotopy "hypothesis" has any chance of being true. Clearly you disagree, so where are the proofs of this homotopy "hypothesis"? Answer: there are none, because as I have said previously, cobordism hypothesis is the cornerstone of something concrete while this homotopy "hypothesis" is the cornerstone of absolute abstract algebraic wank.

>>9518171
Combine rigid motions with inversions.
>>9519772
>local ring variety/scheme/manifold
In particular your example is most concretely realized as a sheave of germs on a Riemannian manifold. Sheaves on paracompact manifolds are the essence of Cousin's theorem for the existence of global sections.
>>9519854
>but no intuition
What do you mean? It's plenty intuitive.

>>9401196
Sounds like what people would gather from skimming Griffith. Go read an actual QM book like Townsend, Sakurai or Landau-Lifshitz.

>>9259763
>no Landau-Lifshitz

>>8758646
>[math]\Delta^k_X \subset W[/math]
What? So [math]W[/math] actually contains the entire diagonal? How can it be open then?

>>8734611
Ok. A lot of these functors aren't clearly defined and I don't see how the sobrification relates to the original space. Anyways what this looks like is a space structure if the functor[math]L:\mathscr{T}\rightarrow \mathscr{S}[/math] is covariant, and it seems to be compatible with disjoint unions and associative/commutative on the nose as well. If we can endow this [math]L[/math]-space structure with a cobordism theory [math](M,L)[/math] then we can define a topological quantum field theory [math](\mathfrak{T}_K,\tau_K)[/math] on it where [math]K[/math] is a ring. Depending on what [math]L[/math] preserves this TQFT can probably tell us something about how locales affect the structure of the modules.

>>8355059
What the flying fuck are conformal blocks? I've been reading about conformal field theory and particle statistics and I have been encountering this nomenclature everywhere in the paper.
I understand that it's basically the conformally invariant part of an n-point correlation function but why is it called a "block"?