We derive a formula for the η-invariants of equivariant Dirac operators on quotients of compact Lie groups, and for their infinitesimally equivariant extensions. As an example, we give some computations for spheres. Quotients M = G/H of compact Lie groups provide many important examples of Riemannian manifolds with non-negative sectional curvature. The primary characteristic classes and numbers...

INTRODUCTION 4 Introduction Zeta functions encoding geometric information such as zeta functions of algebraic varieties over finite fields or zeta functions of finite graphs will loosely be called geometric zeta functions in the sequel. Sometimes the geometric situation gives one tools at hand to prove analytical continuation, functional equation and an adapted form of the Riemann hypothesis. T...

Reuter H, Scholz H: A study of the ion selectivity and the kinetic properties of the calcium-dependent slow inward current in mammalian cardiac muscle. J Physiol (Lond) 264: 17-47, 1977 Singer DH, James TN, Harris P, Malm JR, Hoffman BF: Electrophysiology of chronic atrial fibrillation (abstr). Circulation 36: 239, 1967a Singer DH, Lazzara R, Hoffman BF: Interrelationships between automaticity ...

Let M‾ be a compact smoothly stratified pseudomanifold with boundary, satisfying the Witt assumption. In this paper we introduce de Rham signature and Hodge of M‾, prove their equality. Next, building also on recent work Albin Gell-Redman, extend Atiyah-Patodi-Singer index theory established in our previous under hypothesis that has stratification depth 1 to general case, establishing particula...

In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so–called Kadison–Dubois property. This is used to generalize Jacobi’s version of the Kadison–Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar’s Positivstellensatz. We finish the paper...

We discuss a method of solving n order scalar ordinary differential equations by extending the ideas based on the Prelle-Singer (PS) procedure for second order ordinary differential equations. We also introduce a novel way of generating additional integrals of motion from a single integral. We illustrate the theory for both second and third order equations with suitable examples. Further, we ex...

Zero modes are an essential part of topological field theories, but they frequently also obstacle to the explicit evaluation associated path integrals. In order address this issue in case Ray-Singer Torsion, which appears various gauge we introduce a massive variant Torsion involves determinants twisted Laplacian with mass without zero modes. This has advantage allowing one explicitly keep trac...