Emergent Mind
A-infinity structure on simplicial complexes
(0704.2609)
Published Apr 19, 2007
in
math.GT
,
cs.DM
,
and
hep-th
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.
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