Thurston Vanishing

Michael McQuillan (University of Rome Tor Vergata)

Friday 1st December, 2023 16:00-17:00 Maths 311B


Thurston's method of proof in establishing that rational maps $f$ of $\mathbb{P}^1_{\mathbb{C}}$ with pre-periodic critical points which aren't multiplication on an elliptic curve $\pm 1$ are rigid was
generalised by Adam Epstein to an almost exhaustive local to global theory of deformations of dynamical systems. Indeed arguably its only fault was not to have identified a suitable topus of $f$-equivariant sheaves. Once one remedies this lacuna, natural extensions of Epstein's methods and new results in dynamical systems immediately suggest themselves. En passant we calculate the dualising complex of a real blow up, which is not only a sheaf but a remarkably algebraic one which presents notable opportunities for trivialising the analysis of Stokes' phenomenon. A pre-print is available at:

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