Classification and Characterization of rationally elliptic manifolds in low dimensions

We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy types of closed, simply connected, rationally elliptic 7-manifolds. We give partial results in dimensions 8 and 9.Comment: 23 pages; extended Section 2, revised Section 5 and several minor revision

On the origin of space

Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension $d$ of space evolves smoothly with time in the range 0 <= d(t) <=3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.Comment: 14 pages 3 figures, some clarifications adde

Magnetotransport Properties and Subband Structure of the Two-Dimensional Electron Gas in the Inversion Layer of Hg1-xCdxTe Bicrystals

The electronic and magnetotransport properties of conduction electrons in the grain boundary interface of p-type Hg1-xCdxTe bicrystals are investigated. The results clearly demonstrate the existence of a two-dimensional degenerate n-type inversion layer in the vicinity of the grain boundary. The observed quantum oscillations of the magnetoresistivity result from a superposition of the Shubnikov-de Haas effect in several occupied electric subbands. The occupation of higher subbands is presumable depending on the total carrier density ns of the inversion layer. Electron densities, subband energies, and effective masses of these electric subbands in samples with different total densities are determined. The effective masses of lower subbands are markedly different from the band edge values of the bulk material, their values decrease with decreasing electron density and converging to the bulk values at lower densities. This agrees with predictions of the triangular potential well model and a pronounced nonparabolicity of the energy bands in Hg1-xCdxTe. At high magnetic fields (B > 10 T) it is experimentally verified that the Hall resistivity xy is quantized into integer multiplies of h/e2

The L2L^2-Alexander torsion for Seifert fiber spaces

We calculate the $L^2$-Alexander torsion for Seifert fiber spaces and graph manifolds in terms of the Thurston norm.Comment: 11 pages, 1 figure, fixed a minor mistake in the formulation of Lemma

Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery

Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by using the specific fractional approach an additional factor 2 in accuracy of the derived results.Comment: 5 pages, 3 figures, draft for proceedings IFAC FDA12 in Nanjing, Chin

q-deformed Lie algebras and fractional calculus

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equivalence of rotational and vibrational spectra for fractional q-deformed Lie algebras is shown and the $B_\alpha(E2)$ values for the fractional q-deformed symmetric rotor are calculated.Comment: 8 pages, 3 figure