Proof of the Fukui conjecture via resolution of singularities and related methods: III

摘要

The present article is a direct continuation of the second part of this series. In conjunction with the analysis of the energy band curves of carbon nanotubes, we develop here fundamental theoretical tools, which are essential to prove the Local Analyticity Proposition (LAP). The LAP enables one to prove the Fukui conjecture (the guiding conjecture for developing the repeat space theory) in a new and powerful context of the theory of algebraic curves and resolution of singularities. The present fundamental tools also serve as modular tools for the repeat space theory, by which one can solve a variety of additivity and molecular network problems in a unifying manner. Keywords Fukui conjecture - Repeat space theory (RST) - Additivity problems - Asymptotic linearity theorem (ALT) - Resolution of singularities This article is dedicated to the memory of the late Professors Kenichi Fukui and Haruo Shingu.