A-infinity structure on simplicial complexes

Details A-infinity structure on simplicial complexes A-infinity structure on simplicial complexes

2007-04-19

arxiv.org/abs/0704.2609v5

Mathematics

Geometric Topology

final version. 29 pages

Scientific paper

10.1007/s11232-008-0093-9

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.

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