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.
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