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arXiv · 2308.08369

Torsion volume forms

Florian Naef·Pavel Safronov
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Abstract

We introduce volume forms on mapping stacks in derived algebraic geometry using a parametrized version of the Reidemeister-Turaev torsion. In the case of derived loop stacks we describe this volume form in terms of the Todd class. In the case of mapping stacks from surfaces, we compare it to the symplectic volume form. As an application of these ideas, we construct canonical orientation data for cohomological DT invariants of closed oriented 3-manifolds.

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Florian Naef, Pavel Safronov. 2023-08-16. Torsion volume forms. https://arxiv.org/abs/2308.08369

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