Regularity of analytic torsion form on families of normal coverings

Bing Kwan So; GuangXiang Su

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arXiv · 1405.4631

Regularity of analytic torsion form on families of normal coverings

Bing Kwan So·GuangXiang Su

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Abstract

We prove the smoothness of the L^2-analytic torsion form on some fiber bundles with non-compact fibers of positive Novikov-Shubin invariant. We do so by generalizing the arguments of Azzali-Goette-Schick to an appropriate Sobolev space, and proving that the Novikov-Shubin invariant remains positive in the Sobolev settings, using an argument of Alvarez Lopez-Kordyukov.

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Bing Kwan So, GuangXiang Su. 2014-05-19. Regularity of analytic torsion form on families of normal coverings. https://arxiv.org/abs/1405.4631

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