A bridge between Vector Bundle Theory and Nonlinear Spectral Theory

TL;DR

This paper uncovers deep links between vector bundle theory and nonlinear spectral theory, introducing new invariants related to algebraic multiplicities and orientability using path integration methods.

Contribution

It establishes novel connections between algebraic multiplicities, intersection theory, and vector bundle orientability, providing new invariants via path integration techniques.

Findings

Defined invariants related to the first Stiefel-Whitney class

Connected algebraic multiplicities with vector bundle properties

Introduced path integration methods for invariant computation

Abstract

This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it facilitates the definition of several invariants closely related to the first Stiefel-Whitney fundamental class through some path integration techniques.