Equivariant simplicial reconstruction

Author: 

Carbone, L
Nanda, V
Naqvi, Y

Publication Date: 

14 December 2020

Journal: 

SIAM Journal on Applied Algebra and Geometry

Last Updated: 

2021-03-18T00:15:49.587+00:00

Issue: 

4

Volume: 

4

DOI: 

10.1137/20M1327483

page: 

532-552

abstract: 

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.

Symplectic id: 

1131281

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article