A non-commutative differential module approach to Alexander modules
Aristides Kontogeorgis, Panagiotis Paramantzoglou
TL;DR
This paper introduces a novel approach to Alexander modules using non-commutative differential modules, drawing analogies with cotangent complexes and illustrating with Galois covering examples.
Contribution
It develops a non-commutative differential module framework for Alexander modules, extending Crowell's derived modules and connecting to cotangent complex theory.
Findings
New non-commutative differential module approach to Alexander modules
Analogies established with cotangent complex theory
Examples from Galois coverings of curves
Abstract
The theory of R. Crowell on derived modules is approached within the theory of non-commutative differential modules. We also seek analogies to the theory of cotangent complex from differentials in the commutative ring setting. Finally we give examples motivated from the theory of Galois coverings of curves.
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