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Torsion volume forms

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arxiv 2308.08369 v1 pith:PW7FIL3C submitted 2023-08-16 math.AG math.ATmath.KT

Florian Naef , Pavel Safronov This is my paper · ORCID
classification math.AGmath.ATmath.KT
keywords volumestackscasederivedformformsmappingtorsion
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cohomology of symmetric stacks

    math.AG 2025-02 conditional novelty 8.0 of 10

    A decomposition theorem for cohomology of symmetric stacks yields BPS cohomology, proving cohomological integrality for wide classes of moduli stacks and 3-Calabi-Yau categories.

  2. Adjoint Reidemeister torsion of 3-manifolds with torus boundary for semisimple algebraic groups

    math.GT 2026-02 conditional novelty 7.0 of 10

    Adjoint Reidemeister torsion is defined for semisimple algebraic groups on 3-manifolds with torus boundary, and for hyperbolic manifolds it factors through principal PGL2 embeddings into products of known PGL2 torsions.

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