Heegaard分解理论是三维流形拓扑的重要组成部分。2001年，Hempel利用曲线复形理论引入了Heegaard分解距离的定义，并利用此距离处理了Heegaard分解理论及相关方面的一些问题。本项目以曲线复形理论为基础，提出Heegaard分解的i-距离的概念，并研究这些距离在Heegaard分解理论上的应用。主要内容有：提出Heegaard分解的i-距离的概念，利用这些距离研究三维流形融合等方面的性质，研究不同维数的距离之间的区别及联系。本项目的研究内容是对Heegaard分解距离的一种推广，同时对Heegaard分解理论各相关方面有重要的应用价值。

The theory of Heegaard splittings is an important part of 3-manifold topology. In 2001, Hempel applied the curve complex theory to introduce the distances of Heegaard splittings to deal with some problems in the theory of Heegaard splittings and related topics. Based on the curve complex theory, we define the i-distances of Heegaard splittings and study the applications of these distances on Heegaard splitting theory. The main contents include defining the i-distances of Heegaard splittings, studying the properties of amalgamation of 3-manifolds and detecting the relationships between these distances. The contents of this project generalize the distance of Heegaard splittings and have important application value for related aspects of Heegaard splitting theory.