Equivariant simplicial reconstruction

We introduce and analyze parallelizable algorithms to compress and accurately
reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed
data – called a complex of groups – amounts to a functor from (the poset of simplices in)
the orbit space to the 2-category of groups, whose higher structure is prescribed by isomorphisms arising from conjugation. Using this functor, we show how to algorithmically recover
the original complex up to equivariant simplicial isomorphism. Our algorithms are derived
from generalizations (by Bridson-Haefliger, Carbone-Rips and Corson, among others) of the
classical Bass-Serre theory for reconstructing group actions on trees.