Analytic torsion on spherical factors and tessellations - Mathematics > Differential GeometryReport as inadecuate




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Abstract: The analytic torsion is computed on fixed-point free and non fixed-point freefactors tessellations of the three-sphere. We repeat the standardcomputation on spherical space forms Clifford-Klein spaces by an improvedtechnique. The transformation to a simpler form of the spectral expression ofthe torsion on spherical factors effected by Ray is shown to be more generalthan his derivation implies. It effectively allows the eigenvalues to beconsidered as squares of integers, and applies also to trivial twistings. Theanalytic torsions compute to algebraic numbers, as expected. In the case oficosahedral space, the quaternion twisting gives a torsion proportional to thefundamental unit of Q5^1-2. As well as a direct calculation, the torsionsare obtained from the lens space values by a character inducing procedure.Ontessellations, terms occur due to edge conical singularities.



Author: J.S.Dowker, Peter Chang

Source: https://arxiv.org/







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