This post is a toy investigation of the cluster move as a transformation of skeleta. It contains any new ideas. The cluster move should represent the relationship between opposite ends of a continuous process labeled by a one-parameter family of Morse functions whose skeleta transform by a blow-down, blow-up procedure. Arborealization is realized by the blow-up, so …
Investigating the monodromy of the rank-two sheaf microlocal dual to the complex Lagrangian brane $L = \{y = \pm \sqrt{x}\} \subset T^*\mathbb C_x$, we follow the family $hom_{Fuk}(L,T^*_{x = e^{2\pi i t}}\mathbb C)$ of cochain complexes as $t$ goes from $0$ to $1.$ To compute, we turn our heads and consider that $L = \{ …
Sections 8.3 and 8.4 of this http://arxiv.org/pdf/1303.3253v4.pdf (which were in a book that appeared in my mailbox) are a short (dense) summary of Stokes moduli spaces and their different incarnations. The paper surely has loads of gems, but is about as scattered and unstructured as this blog.
I’m uploading this page summarizing a talk I gave. trefoil-hitchin-onepage