We develop a finite KK-theory of C∗-algebras following ArlettazH.Inassaridze’s approach to finite algebraic K-theory [1] . The BrowderKaroubi-Lambre’s theorem on the orders of the elements for finite algebraic K-theory [ , ] is extended to finite KK-theory. A new bivariant theory, called torsion KK-theory is defined as the direct limit of finite KK-theories. Such bivariant K-theory has almost a...

2 We discuss the theoretical basis for the search of the possible experimental manifestations of the torsion field at low energies. First, the quantum field theory in an external gravitational field with torsion is reviewed. The renormalizability requires the nonminimal interaction of tor-sion with spinor and scalar (Higgs) fields. The Pauli-like equation contains new torsion-dependent terms wh...

The shifted quantization condition of the M-theory 4-form G4 is well-known. The most naive generalization to type IIA string theory fails, an orientifold fourplane counterexample was found by Hori in hep-th/9805141. In this note we use D2-brane anomaly cancellation to find the corresponding shifted quantitization condition in IIA. Our analysis is consistent with the known O4-plane tensions if w...

We investigate a linearized tensor-tensor theory of gravity with torsion and a perturbed torsion wave solution is discovered in background Minkowski spacetime with zero torsion. Furthermore, gauge transformations of any perturbed tensor field are derived in general background non-Riemannian geometries. By calculating autoparallel deviations, both longitudinal and transverse polarizations of the...

The Chern isomorphism determines the free part of the K-groups from ordinary cohomology. Thus to really understand the implications of K-theory for physics one must look at manifolds with K-torsion. Unfortunately there are not many explicit examples, and usually for very symmetric spaces. Cartesian products of RPn are examples where the order of the torsion part differs between K-theory and ord...

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

In this paper, we study lower bounds on the K-theory of the maximal C∗-algebra of a discrete group based on the amount of torsion it contains. We call this the finite part of the operator K-theory and give a lower bound that is valid for a large class of groups, called the “finitely embeddable groups”. The class of finitely embeddable groups includes all residually finite groups, amenable group...

The C* -algebra extensions of a topological space can be made into an abelian group which is naturally equivalent to the Khomology group of odd dimension [1] which has a close relation with index theory and is one of the starting points of KK theory [8]. The Cp -smoothness of an extension of a manifold was introduced in [3, 4], where Cp denotes the Schatten-von Neumann p-class [5]. We generaliz...

We consider deformations of torsion-freeG2 structures, defined by theG2-invariant 3-form φ and compute the expansion of ∗φ to fourth order in the deformations of φ. By considering M -theory compactified on a G2 manifold, the G2 moduli space is naturally complexified, and we get a Kähler metric on it. Using the expansion of ∗φ we work out the full curvature of this metric and relate it to the Yu...