This is a research discussion board about constructible sheaves and microlocal geometry, especially in terms of its role as a model for the Fukaya category. Here you will find posts by many people, including: Xin Jin, Andy Neitzke, Lenhard Ng, Dan Rutherford, Vivek Shende, Steven Sivek, Alex Takeda, David Treumann, Harold Williams, and Eric Zaslow. Some of the …
What’s the point of always adjoining Maurer-Cartan elements?
We are having a small discussion group around Tamarkin’s paper “microlocal category”. There will be a blog post for each chapter, in which we collect together our understandings and misunderstandings. At the moment they are mostly empty. This is the post for chapter 1.
Question: What’s the sheaf theoretic incarnation of this filtration? (Warmup question: what structure does a filtration on a DGA induce on its representation category?)
Let $M$ be a manifold; $shv(M)$ the (derived) category of sheaves on $M$, and $\mathcal{G}(M)$ the group of autoequivalences of $shv(M)$. I want to consider the following sort of right-invariant semi-metric (i.e. some things have distance zero) on $\mathcal{G}(M)$: $$d(\gamma, \eta) = sup_{F} d_{Haus}(ss(\gamma F), ss( \eta F))$$ Here, we take $ss(F)$ in the cosphere bundle …