BFV-复形的不变性
Invariance of the BFV-complex
摘要：
BFV-形式主义被引入来处理配备对称性的经典系统。它将微分分次Poisson代数与Poisson流形$(M,Π)$的任何共迷向子流形$S$联系起来。然而，分配（共各向同性子流形）$\leadsto$（微分分次泊松代数）是不规范的，因为在建设几个选择必须作出。一个必须修复：1.将$S$的正常束$NS$嵌入到$M$中，2. $NS$上的连接$\nabla$，以及3.特殊元素$Ω$。我们表明，不同的选择的连接和$Ω$ -但与管状邻域固定-导致同构微分分次泊松代数。如果管状邻域也改变了，则可以在胚芽水平上恢复不变性。
英文摘要：
The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,Π)$. However the assignment (coisotropic submanifold) $\leadsto$ (differential graded Poisson algebra) is not canonical, since in the construction several choices have to be made. One has to fix: 1. an embedding of the normal bundle $NS$ of $S$ into $M$, 2. a connection $\nabla$ on $NS$ and 3. a special element $Ω$. We show that different choices of the connection and $Ω$ -- but with the tubular neighbourhood fixed -- lead to isomorphic differential graded Poisson algebras. If the tubular neighbourhood is changed too, invariance can be restored at the level of germs.
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