Remind me to write a piece on group representation and description by relations

but as it turns out (I think it's a result by Arnol'd but don't quote me on that), if you know an implicit equation that generates the hypersurface, you can simply compute the R-codimension of the implicit equation!

the thing about the Milnor number is that, when you have a hypersurface with isolated singularities, it can be retracted into a bouquet (a wedge of k-spheres) around those singularities

the number of spheres is called the milnor number, and the canonical way to compute it is, well, compute the homology :⁾

i mean ig it makes sense when you consider (x,y²) is just the reflection map

seems like every time you have something in the form (x,y²,something of order ≥ 2) the Tjurina number is 3, regardless

lazy enough to open Singular, distrustful enough to check if I'm doing something wrong for getting the same answer all the time

Chapter 1: The extended $$\mathcal{R}$$-codimension of a function is called the Milnor number!

Chapter 8: Actually, the Milnor number is something different but it just so happens to match........

me: *has stuff to do*
me: let's study the proof of the Darboux theorem

I don't always come here to post, but when I do I suddenly make a long thread filled to the brim with a lax style and lots of slang

the other day I was thinking about how much I always enjoyed puzzle games and I think that's kind of how I ended up in pure math tbh

this clicked after my advisor said in a meeting that the important part of a theorem is chasing after a proof, that you just add the hypotheses later

or $$Df_a$$ if you like the uppercase D but like

they're sophomores give them a break

In this house we only write $$df_a$$

Me: there is no way students don't get confused with this shit

Students: [get confused with that shit and think Df is a function]

Me: figures

Someone: writes $$Df(a)$$ for the differential of $$f$$ at $$a$$

Me: [loud moan]

@ZevenKorian Perhaps it has something to do with the rotational symmetry of Minkowski space?

I thought "well maybe it's because if you have a local isometry--" but the minkowski space is not isometric to the sphere?

I just cheated and looked it up on wikipedia (don't do this at home kids!) and it seems like they coincide on the minkowski space, on S², on...

today in "i could study or I could check this stupid thing my advisors said"

one of my advisors called the Hamilton vector fields "Killing", but Killing vector fields are the solutions of the equation $$\mathcal{L}_\xi g=0$$ (g is the metric tensor)

Truth is subjective.
The children think I've put a climbing frame in the garden.
From my perspective, I've increased the genus of my mowing surface.

ignore that you've seen nothing

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