The quantum Johnson homomorphism and symplectomorphism of 3-folds

Abstract

introduce a subset K2,A of the symplectic mapping class group, and an invariant ... that associates a characteristic class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar Johnson kernel X9 and second Johnson homomorphism - 2 from low-dimensional topology. The method is quite general, and unlike many abstract tools, explicitly computable in certain nice cases. As an application, we prove the existence of symplectomorphism ... of infinite order in symplectic mapping class group ... where Y is the blow-up of P3 at a genus 4 curve. The classical connection between such Fano varieties and cubic 3-folds allows us to factor ... as a product of six-dimensional generalized Dehn twists.