Suppose M is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological torsion of M and the L2-analytic torsion of the Riemannian manifold M are equal. In particular, the L2-topological torsion of M is proportional to the hyperbolic volume of M , with a constant of proportionality w...

LetG be a finite group acting on a Riemannian manifoldM by isometries. We introduce analytic torsion ρan(M,M1;V ) ∈ R⊗Z RepR(G) PL-torsion ρpl(M,M1;V ) ∈ K1(RG) Poincaré torsion ρpd(M,M1;V ) ∈ K1(RG) and Euler characteristic χ(M,M1;V ) ∈ RepR(G) for ∂M the disjoint union of M1 and M2 and V an equivariant coefficient system. The analytic torsionis defined in terms of the spectrum of the Laplace ...

We analyse a spin precession of slow neutrons in the Einstein–Cartan gravity with torsion, chameleon and magnetic field. For the derivation of the Heisenberg equation of motion of the neutron spin we use the effective low–energy potential, derived by Ivanov and Wellenzohn (Phys. Rev. D 92, 125004 (2015)) for slow neutrons, coupled to gravitational, chameleon and torsion fields to order 1/m, whe...

In this paper we use the results of our previous work [FT] in order to compute the phase of the torsion of an Euler structure ξ in terms of the characteristic class c(ξ). Also, we introduce here a new notion of an absolute torsion, which does not require a choice of any additional topological information (like an Euler structure). We prove that in the case of closed 3-manifolds obtained by 0-su...

Let $M$ be a closed spin manifold which supports positive scalar curvature metric. The set of concordance classes metrics on forms an abelian group $P(M)$ after fixing measures the size space $M$. Weinberger and Yu gave lower bound rank in terms number torsion elements $\pi_1(M)$. In this paper, we give sharper by studying image relative higher index map from to real K-theory $\mathrm{C}^\ast$-...

We develop a theory in which there are couplings amongst Dirac spinor, dilaton and non-Riemannian gravity and explore the nature of connection-induced dilaton couplings to gravity and Dirac spinor when the theory is reformulated in terms of the Levi-Civita connection. After presenting some exact solutions without spinors, we investigate the minimal spinor couplings to the model and in conclusio...

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. ...

We propose a refinement of the Ray-Singer torsion, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. Given a closed, oriented manifold of odd dimension with fundamental group Γ, the refined torsion is a complex valued, holomorphic function defined for representations of Γ which are close to the space of unitary representations. When the re...

Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...

A highly efficient catalyst, MoV(0.3)Te(0.17)Nb(0.12)O, used for acrylic acid (AA) production from propane, was used as an anodic catalyst in an SOFC reactor, from which AA and electric power were cogenerated at 400-450 degrees C.