We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then is Fredholm. This generalizes a theorem due to B\"ar-Strohmaier in case of finite times, and we also show corresponding index formula extends setting. Furthermore, demonstrate existe...

We will show that the famous, intractible 1959 Kadison-Singer problem in C∗-algebras is equivalent to fundamental unsolved problems in a dozen areas of research in pure mathematics, applied mathematics and Engineering. This gives all these areas common ground on which to interact as well as explaining why each of these areas has volumes of literature on their respective problems without a satis...

Abstract Relations between the Atiyah–Patodi–Singer rho invariant and signatures of links have been known for a long time, but they were only partially investigated. In order to explore them further, we develop versatile cut-and-paste formula invariant, which allows us manipulate manifolds in convenient way. With help this tool, give description multivariable signature link $L$ as some closed t...