Jason (jcreed) wrote,

There were some leftover concepts from Steve's talk last Friday that I had been meaning to look up on wikipedia and familiarize myself with some more. Mostly it was definitions about bundles and fibrations and covering spaces and stuff like that. In the process of trying to teach myself about them, I stumbled across the definition of Torsors, which besides having an awesome name, are awesome things. They are to groups what affine spaces are to linear spaces. An affine space is a linear space that's forgotten its origin, and a G-torsor is a copy of G that's forgotten where its identity is. Actually what it is is a set X with a G-action that is "free" and "transitive", which as far as I can tell are funny ways of saying "injective" and "surjective". I mean, if you fix an element of x, the group action is just a function, and I think that's what the definitions come out as. Anyway these things that baffle one's otherwise concrete notions about distinguished elements of algebraic structures by sort of quotienting over the whole issue always fascinate me.
Tags: math
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