This paper gives a short summary of the central role played by Ed Brown’s “twisted cochains” in higher Franz-Reidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisted cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR torsi...

This paper gives a short summary of the central role played by Ed Brown’s “twisting cochains” in higher FranzReidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a twisting cochain which is unique up to fiberwise homotopy equivalence. However, when they are based, the difference between two of them is a higher algebraic K-theory class measured by higher FR tors...

After a historical discussion of Einstein’s 1907 principle of equivalence, a homogeneous gravitational field in Minkowski spacetime is constructed. It is pointed out that the reference frames in gravitational theory can be understood as spaces with a flat connection and torsion defined through teleparallelism. This kind of torsion was introduced by Einstein in 1928. The concept of torsion is di...

We study massless Duffin-Kemmer-Petiau (DKP) fields in the context of Einstein-Cartan gravitation theory. In the case of an identically vanishing torsion (Riemannian space-times) we show that there exists local gauge symmetries which reproduce the usual gauge symmetries for the massless scalar and electromagnetic fields. On the other hand, similarly to what happens with the Maxwell theory, a no...

The Floer homology can be trivial in many variants of the Floer theory; it is therefore interesting to consider more refined invariants of the Floer complex. We consider one such instance—the Reidemeister torsion τF of the Floer complex of (possibly non-hamiltonian) symplectomorphisms. τF turns out not to be invariant under hamiltonian isotopies, but we introduce a “correction term”—the Floerth...