A-infinity structure on simplicial complexes

Understand

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds.

• Various operations are explicitly defined on these forms, including exterior derivative and exterior product.
• The latter one is non-associative.
• Instead, as anticipated, it is a part of non-trivial A-infinity structure, involving a chain of poly-linear operations, constrained by nilpotency relation: (d + \wedge + m + ...)^n = 0 with n=2.