Hannah 🍀 @ZevenKorian@mathstodon.xyz

When you see \(\cong\mathbb{K}^{nm}\) and you immediately think "ok, there has to be a matrix somewhere"

http://www.jonathancrabtree.com/mathematics/why-do-negative-numbers-appear-to-the-left-of-zero-and-positive-numbers-to-the-right-of-zero/

(The natural lifting of \(\omega \in \Lambda^1(M)\) is \(\mathcal{L}_1\omega\), where \(1: TM \longrightarrow TM\) is the identity map.)

I spent a ridiculous amount of time trying to find the natural lifting of \(dz-x_1\,dy^1+\dots+x_n\,dy^n\)

Watch "A Different Way to Solve Quadratic Equations" on YouTube - A Different Way to Solve Quadratic Equations: https://youtu.be/ZBalWWHYFQc

Here we go again

You have to love how this paper basically forced the fᵤ and fᵥ notation for partial derivatives just by saying

no, I cannot derivate on any given manifold

but you know what I can do? this

*deep fried df(∂u) and df(∂v)*

Oh boy the explanation of what the Thom-Boardman symbols are is rather complicated here. I think it's time to whip out my good ol' friend Gibson...

my notes are very sloppy in general lol you can tell they are /by/ me and /for/ me as I skip everything I remember from last year and carefully explain everything I didn't understand the first time I read it...

whatever gets into the final thesis is going to need a serious revision but I hope I can explain the concepts more clearly by then

I'm not totally into ᵣJᵏ(n,p) as notation because the ᵣ makes it hard to handwrite the symbol and the author of this book keeps getting the ᵣ everywhere else lol because of course latex assumes it's a subindex for whatever you wrote /before/, not /after/

Another suggestion is https://g.co/kgs/fktbUb

This one seems to go deeper and (I assume) is more complete as a reference. It uses techniques from sheaf theory.

Source:
https://mathoverflow.net/questions/31395/functions-of-several-complex-variables-book-recommendations

Sorry: https://www.jirka.org/scv/

Going to make this into a thread in case someone else is interested. I found this book which seems to be an introduction to the subject written *for* a particular course. Also, CC BY-NC-SA (kudos to Jiří Lebl!)

There is a thread on mathoverflow (https://mathoverflow.net/questions/31395/functions-of-several-complex-variables-book-recommendations) but I ask here anyway in case someone is familiar with the subject

Do you know a book on several complex variables I can use for reference? Basically to check when the rules IRⁿ can be applied to Cⁿ (e.g. Hadamard's lemma apparently holds in Cⁿ)

The proofs being complicated is not a problem as I don't think I will read them; I've been told several complex variables is a tough branch of complex analysis.