论文标题
F-manifolds和信息的几何形状
F-manifolds and geometry of information
论文作者
论文摘要
$ f $ manifolds的理论，更普遍地是在各种涉及代数和分析几何学的量子场理论模型中发现并形成了具有交换性和切线场的交互性乘法的流形，至少是自1990年代以来。 本文的重点是演示，即至少自1960年代以来定义和研究的各种概率分布空间也携带$ f $ - manifolds的自然结构。 这个事实仍然隐藏在广阔的信息存储和传输模型领域的各个领域中，这些领域进行了简要调查。
The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since 1990's. The focus of this paper consists in the demonstration that various spaces of probability distributions defined and studied at least since 1960's also carry natural structures of $F$-manifolds. This fact remained somewhat hidden in various domains of the vast territory of models of information storing and transmission that are briefly surveyed here.
