An A∞ structure on simplicial complexes

被引：3
|
作者：
Dolotin, V. V. [1 ]
Morozov, A. Yu. [1 ]
Shakirov, Sh. R. [1 ]
机构：
[1] Inst Theoret & Expt Phys, Moscow 117259, Russia
来源：
THEORETICAL AND MATHEMATICAL PHYSICS | 2008年 / 156卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
simplicial complex; topology; discrete exterior form; infinity structure;
D O I：
10.1007/s11232-008-0093-9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider a discrete (finite-difference) analogue of differential forms defined on simplicial complexes, in particular, on triangulations of smooth manifolds. Variations operations are explicitly defined on these forms including the exterior differential d and the exterior product boolean AND. The exterior product is nonassociative but satisfies a more general relation, the so-called A(infinity) structure. This structure includes an infinite set of operations constrained by the nilpotency relation (d + boolean AND + m + ...)(n) = 0 of the second degree, n = 2.
引用
收藏
页码：965 / 995
页数：31
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