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An A ∞ structure on simplicial complexes

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We consider a discrete (finite-difference) analogue of differential forms defined on simplicial complexes, in particular, on triangulations of smooth manifolds. Various operations are explicitly defined on these forms including the exterior differential d and the exterior product ∧. The exterior product is nonassociative but satisfies a more general relation, the so-called A ∞ structure. This structure includes an infinite set of operations constrained by the nilpotency relation (d + ∧ + m + …)n = 0 of the second degree, n = 2.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    V. V. Dolotin, A. Yu. Morozov & Sh. R. Shakirov

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  1. V. V. Dolotin
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  2. A. Yu. Morozov
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  3. Sh. R. Shakirov
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Correspondence to V. V. Dolotin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 3–37, July, 2008.

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Dolotin, V.V., Morozov, A.Y. & Shakirov, S.R. An A ∞ structure on simplicial complexes. Theor Math Phys 156, 965–995 (2008). https://doi.org/10.1007/s11232-008-0093-9

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