Reconstructing under group actions

Abstract

We give a bound on the reconstructibility of an action G → X in terms of the reconstructibility of a the action N → X, where N is a normal subgroup of G, and the reconstructibility of the quotient G/N. We also show that if the action G → X is locally finite, in the sense that every point is either in an orbit by itself or has finite stabilizer, then the reconstructibility of G → X is at most the reconstructibility of G. Finally, we give some applications to geometric reconstruction problems. © Springer-Verlag Berlin Heidelberg 2006.