%0 Journal Article %A López Gómez, Julián %A Sampedro Pascual, Juan Carlos %T Orientability through the algebraic multiplicity %D 2023 %@ 1661-7738 %U https://hdl.handle.net/20.500.14352/104970 %X This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, χ, 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 characteristic class through some path integration techniques. %~