A bridge between Vector Bundle Theory and Nonlinear Spectral Theory

2022/01/16 by Julián López-Gómez, López-Gómez, Julián, Juan Carlos Sampedro +1
Computer Science · Engineering · #47H11 #55R50 #58C40 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #K-Theory and Homology (math.KT) #Polynomial and algebraic computation #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2201.05949

openalex publication_date 2022/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Vector bundles, linear representations, and spectral problems
• New Analytical and Geometrical Aspects of the Algebraic Multiplicity
• Spectral Theory and Bezout Theorem
• Geometric Invariant Theory, holomorphic vector bundles and the Harder-Narasimhan filtration
• Algebraic stacks