Wheeled PROPs, graph complexes and the master equation
Wheeled PROPs, graph complexes and the master equation
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轮式 PROP、复合图形和主方程
DOI：
10.1016/j.jpaa.2008.08.007
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发表时间：
2006
影响因子：
0.8
通讯作者：
Sergei Shadrin
中科院分区：
文献类型：
--
作者：
Martin Markl;Sergei Merkulov;Sergei Shadrin
我们介绍并研究轮式 PROP，这是 PROP 理论的扩展，它可以处理迹，特别是涉及散度算子的主方程的解。我们构造了一个 dg 自由轮 PROP，其表示与 SP 流形的形式胚一一对应，SP 流形是 Batalin-Vilkovisky 量子化理论中的关键几何对象。我们还构建了经典操作数 Com 和 Ass 的最小轮式分辨率，作为众所周知的 dg 操作数 Com 和 Ass 的非平凡扩展。最后，我们将上述结果应用于 Kontsevich 复形带状图有向版本的上同调计算。
We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in one-to-one correspondence with formal germs of SP-manifolds, key geometric objects in the theory of Batalin–Vilkovisky quantization. We also construct minimal wheeled resolutions of classical operads Com and Ass as non-trivial extensions of the well-known dg operads Com∞and Ass∞. Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich’s complex of ribbon graphs.