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🔥 Top post: Add up the volumes of the simplices in all dimensions. The sum i · 23 likes + reposts
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There is a somewhat mysterious relationship between the trefoil knot and the 3-dimensional associahedron that was observed by Loday. Basically, there is a natural way of drawing the trefoil knot on the associahedron. Reverse engineering th…
https://mathoverflow.net/questions/468011/what-is-the-image-of-a-smooth-map
https://mathoverflow.net/questions/463056/equivalence-class-of-parametrized-surfaces-which-induce-the-same-current
Elliot Cheung: Towards a discretization of Chern-Simons theory
https://youtu.be/qRJKkSE2woU?si=kuTTIhnjfsFOqS-u
Along the way, I also talk about stacks as Lie groupoids up to Morita equivalence, as well as the infinitesimal counterpart to groupoids: Lie algebroids.
4/4
This time, I look at the other side of the story: how to encode a quotient stack in terms of an L-infinity algebra which is concentrated in degrees 0 and 1.
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In the first part, I told you how the 'derived' zero locus of a function can be encoded by an L-infinity algebra which is concentrated in degrees 1 and 2.
https://francisrlb.com/2023/02/25/how-does-a-lie-algebra-encode-a-space-part-1/
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Finally! The long-awaited sequel in my series of blog posts: How does a Lie algebra encode a space?
https://francisrlb.com/2023/07/29/how-does-a-lie-algebra-encode-a-space-part-2/
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Reference request for Whitehead lemma:
https://mathoverflow.net/questions/451324/reference-request-whiteheads-lemma-for-semisimple-lie-algebras
In the paper, I also take a closer look at this extension problem and relate it to the study of vector bundles on weighted projective space. 8/8
The cool thing is that the subcategories of connections that *do* extend over the entire vector space are not the same on either side of a castling equivalence. Hence, this gives a very simple method for producing examples of non-extendabl…
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