Year: 2026
Type: article
Abstract: Ghost modules were introduced in [K. Igusa, Generalized Grassmann invariant-redrawn, arXiv 2502.19147] without definitions or proofs. We also introduced stability diagrams or “relative pictures” for torsion classes and torsion-free classes for representations of Dynkin quivers. Modules which were not in the chosen class reappeared as “ghosts”, in fact one missing module produced two ghosts. In this short paper, we give a precise definition of ghost modules. We give several examples and prove basis properties of ghosts and pictures for torsion and torsion-free classes. We also introduce a third kind of ghost which we call “extension ghosts”. In the next paper we will explain how these new ghosts can be used to visualize the computation of the higher Reidemeister torsion carried out in [K. Igusa and J. Klein, The Borel regulator map on pictures, II: An example from Morse theory, K-Theory 7(3) (1993) 225–267].
Author: Kiyoshi Igusa
Institution: Brandeis University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Simons Foundation
Award: G7075666560
OpenAlex ID: W4415117789