
chloe
16.8K posts

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im @schala163@mathstodon.xyz on mastodon and u should follow me in case twitter explodes pls
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@TimHenke9 @littmath right. The gluing data is a cocycle with values in GL_n which is a very precise sense in which keeping track of the isomorphisms between fibers encodes all the interesting information in this example
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@schala163 @littmath yeah, vector bundles were also what I was naturally thinking of, but I couldn't find a punchy way of saying it
like here of course the information is just hidden in the gluings
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@TimHenke9 @littmath if you glue a bunch of trivial vector bundles on an open cover you get a trivial vector bundle, but if you glue a bunch of trivializable vector bundles you can get an vector bundle (at least in some contexts)
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@littmath Do you have a sharp, short argument that shows the absolute necessity?
I've tried before to argue the importance of the difference between trivial and trivialisable but found that I didn't really find the right example
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@kirbykaze_ i believe it is literally impossible to get a good fastfall timing on AC nair with making some unreactable assumption about which parts of the move are going to induce hitlag, which imo is neat
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@AdithyaRao @QiaochuYuan no they didn't. That's not true actually. Before Euclid nobody knew anything about Euclidean geometry, if you can even believe it.
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@JDHamkins the induced map on the 0'th exterior power of a 0-dimensional vector space is the identity 🥰
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@QiaochuYuan @UntilTrees The other one should be something like the smallest fixed point of the map that sends alpha to the "alpha'th church-kleene ordinal" (by which I mean the smallest ordinal whose order type is not computable by an ordinal turing machine up to rank alpha)
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people get fucked up about godel's incompleteness theorems but it's worth spending some time getting fucked up about tarski's undefinability theorem. it is not totally wrong to summarize it as "it is not possible to define truth." isn't that interesting? worth a thonk

Wolf Tivy@wolftivy
Do you consider the theological implications of CS and math theorems, anon? Post your best take on the theology of mathematical foundations or we’ll deport you to the humanist gibberish department.
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@pythagoreancat there's a version of gauss-bonnet for orbifold surfaces that reduces to this formula when the metric is flat (so all the curvature comes from orbifold points) and reduces to the usual gauss-bonnet theorem when there are no orbifold points
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