FoxDifferential.Completed.Residue.FreeGroup

5 sections | 5 files | 31 declarations

Crossed differentials, universal differential modules, Fox boundaries, Euler formulas, and Jacobians are the common algebraic layer used by Crowell and metabelian applications.

Basic

1 files | 10 declarations | 7 Theorem | 2 Definition | 1 Abbreviation

Residue Fox-coordinate vectors with coefficients in \((\mathbb{Z}/n\mathbb{Z})[H]\).

Boundary

1 files | 3 declarations | 2 Theorem | 1 Definition

The residue Fox boundary/Euler map \(v \mapsto \sum_i v_i * ([\psi(x_i)]-1)\).

Coordinates

1 files | 8 declarations | 5 Theorem | 3 Definition

The linear map from the residue universal module to residue Fox-coordinate vectors.

Fundamental

1 files | 6 declarations | 6 Theorem

Boundary-map form of the residue Fox fundamental formula.

Universal

1 files | 4 declarations | 2 Theorem | 2 Definition

Residue crossed differentials on a free group are represented by the corresponding universal residue module.