A-infinity structure on simplicial complexes
Geometric Topology
2009-11-13 v5 Discrete Mathematics
High Energy Physics - Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0704.2609,
title = {A-infinity structure on simplicial complexes},
author = {V. Dolotin and A. Morozov and Sh. Shakirov},
journal= {arXiv preprint arXiv:0704.2609},
year = {2009}
}