We give explicit formulae for differential graded Lie algebra (DGLA) models of -cells. In particular, for a cube and an -faceted banana-shaped -cell with two vertices, edges each joining those two vertices, and bi-gon -cells, we construct a model symmetric under the geometric symmetries of the cell fixing two antipodal vertices. The cube model is to be used in forthcoming work for discrete analogues of differential geometry on cubulated manifolds.
Bibliographical noteFunding Information:
Received by the editors February 27, 2020. Published online on Cambridge Core July 1, 2020. is research was supported in part by Grant No. 2016219. from the United States-Israel Binational Science Foundation (BSF). Griniasty is grateful to the Azrieli Foundation for the award of an Azrieli Fellowship. AMS subject classification: 17B55, 17B01, 55U15. Keywords: DGLA, Maurer–Cartan, Baker–Campbell–Hausdorff formula.
- AMS subject classification 17B55 17B01 55U15