AI 中文总结
本文重论辛几何中的马斯洛夫指标，在已有四种定义方法的基础上提出两种新方法，并与Her和Zhong基于早期工作定义的辛矩阵路径不变量进行了比较。
AI 中文摘要
三十年前，在《关于马斯洛夫指标》一文中，本文作者与已故的耶鲁大学罗尼·李教授合作，给出了马斯洛夫指标的公理化定义，该指标是拉格朗日对的连续分段光滑路径的整数值不变量。文中给出了四种不同的马斯洛夫指标定义方法，每种方法都满足相关公理。本文在此基础上又提出了两种新的定义方法，并与赫尔（Her）和钟（Zhong）基于利德斯基（Lidskii）、格尔范德（Gelfand）、萨洛蒙（Salomon）以及泽恩德（Zehnder）早期工作所定义的辛矩阵路径不变量进行了比较。
英文摘要
Thirty years ago in ``On the Maslov Index'' the present authors with their late collaborator Prof. Ronnie Lee of Yale University presented an axiomatization of the Maslov index, an integer-valued invariant of continuous, piecewise smooth paths of pairs of Lagrangians. Four distinct methods of definition of such Maslov indicies were given; each satisfying the axioms. Here two more are offered and comparisons are made to the recent work of Her and Zhong defining an invariant of a path of symplectic matrices motivated by earlier work of Lidskii and Gelfand, Salomon and Zehnder.
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