Group Actions from Algebraic Flops

This paper constructs derived autoequivalences associated to an algebraic flopping contraction $X\to X_{\con},$ where $X$ is quasi-projective with only mild singularities. These functors are constructed naturally using bimodule cones, and we prove these cones are locally two-sided tilting complexes by using the local-global properties and a key commutative diagram. The main result is that these autoequivalences combine to give an action of the fundamental group of an associated infinite hyperplane arrangement on the derived category of $X.$ This generalises and simplifies \cite{DW3}, by finally removing reliance on subgroups, and it also lifts many other results from the complete local setting.