Partial Signatures and the Yoshida-Nicolaescu Theorem

TL;DR

This paper provides a straightforward proof of the Yoshida-Nicolaescu Theorem using partial signatures, extending its applicability by removing the non-degeneracy condition at endpoints and redefining the Maslov index.

Contribution

It introduces a simplified, more general proof of the Yoshida-Nicolaescu Theorem utilizing partial signatures and a natural Maslov index definition.

Findings

Proof of the Yoshida-Nicolaescu Theorem without endpoint non-degeneracy

Extension of the theorem to a broader context using partial signatures

A new, natural definition of the Maslov index

Abstract

In this article, we give a simple and direct proof of the Yoshida-Nicolaescu Theorem in a more general context by using the theory of partial signatures. We do not impose the usual condition of non-degeneracy at the endpoints and use a natural definition of the Maslov index.