Let p:M → B be a family of compact manifolds equipped with a unitarily flat vector bundle F → M . We generalize Igusa’s higher Franz-Reidemeister torsion τ(M/B;F ) to the case that the fibre-wise cohomologyH(M/B;F ) → B carries a parallel metric. If moreover M admits a fibre-wise Morse function, we compute the difference of τ(M/B;F ) and the higher analytic torsion T (M/B;F ). We also generalis...

Starting with topological field theories we investigate the Ray-Singer analytic torsion in three dimensions. For the lens Spaces L(p; q) an explicit analytic continuation of the appropriate zeta functions is contructed and implemented. Among the results obtained are closed formulae for the individual determinants involved, the large p behaviour of the determinants and the torsion, as well as an...

Torsion, topology and CPT anomaly in two-dimensional chiral U (1) gauge theory Abstract We consider the CPT anomaly of two-dimensional chiral U (1) gauge theory on a torus with topologically nontrivial zweibeins corresponding to the presence of spacetime torsion. The resulting chiral determinant can be expressed in terms of the standard chiral determinant without torsion, but with modified spin...

The main object of this note is to study the conormal module M and the computation of the second symbolic power ḡ of an ideal ḡ in the residue ring O/h of a polynomial ring O over a field of characteristic zero. The torsion part T (M) of M and the torsion free module M/T (M) are expressed by the primitive ideal of g relative to h. Two characterizations for M/T (M) to be free are proved. Some im...

This article presents theoretical arguments that certain virtual bound states carry the trace component of affine torsion. The motivation for this work is Einstein Cartan theory, which extends general relativity by including torsion to model intrinsic angular momentum, becoming more credible. author not aware any situation there evidence or substantial argument presence trace, except in continu...

The study of modules over a finite von Neumann algebra A can be advanced by the use of torsion theories. In this work, some torsion theories for A are presented, compared and studied. In particular, we prove that the torsion theory (T,P) (in which a module is torsion if it is zero-dimensional) is equal to both Lambek and Goldie torsion theories for A. Using torsion theories, we describe the inj...

In two previous papers with Yi-Jen Lee, we defined and computed a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. The present paper gives an a priori proof that this Morse theory invariant is a topological invariant. It is hoped that this will provide a model for possible generalizations to Floer theory. In two papers with Yi-Jen Lee [HL1,...

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexity of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3 ≤ m < n and p, q are distinct primes, the...

Introduction: The aim was to investigate the protective effect of the Syzygium aromaticum extract on damaged tissues and the oxidative stress after testicular torsion.&nbsp;Methods: Rats were randomly divided into a control group subjected to a sham procedure and three treatment groups comprising testicular torsion followed by detorsion (TD), testicular torsion detorsion followed by the tre...