English

Torsion volume forms

Algebraic Geometry 2023-08-17 v1 Algebraic Topology K-Theory and Homology

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.

Keywords

Cite

@article{arxiv.2308.08369,
  title  = {Torsion volume forms},
  author = {Florian Naef and Pavel Safronov},
  journal= {arXiv preprint arXiv:2308.08369},
  year   = {2023}
}

Comments

58 pages

R2 v1 2026-06-28T11:57:02.757Z