Euler isomorphism, Euler basis, and Reidemeister torsion

The aim of these notes is to present a general algebraic setting based on the Euler isomorphism for complexes of vector spaces as in the book by Gelfand, Kapranov, and Zelevinsky, and on some self duality properties of graded vector spaces that completely characterises the combinatorial invariants of Reidemeister torsion and Reidemeister metric. The work has been inspired by papers of Farber and Farber and Turaev, who originally considered this approach to Reidemeister torsion, and by subsequent work of M. Braverman and Kappeler.