Vol. 10, No. 1, 2020

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Effective computation of degree bounded minimal models of GCDAs

Victor Manero and Miguel Á. Marco Buzunáriz

Vol. 10 (2020), 25–39
DOI: 10.2140/jsag.2020.10.25

Given a finitely presented graded commutative differential algebra (GCDA), we present a method to compute its minimal model up to a specified degree, together with a map that is a quasi-isomorphism up to the given degree. The method works by adding generators one by one. It terminates if and only if the minimal model is finitely generated up to the given degree. A specific implementation of the method is given.

The method allows us to develop and implement two criteria for i-formality, one necessary and one sufficient. These criteria can be checked effectively, and have been able to determine the i-formality for every example that we have tested.

graded commutative algebras, minimal model, formality, sagemath
Mathematical Subject Classification 2010
Primary: 53-04, 55-04
Supplementary material

A python package for commutative differential graded algebra computations using Sage

Received: 27 September 2019
Revised: 26 March 2020
Accepted: 21 April 2020
Published: 2 May 2020
Victor Manero
Departamento de matemáticas – I.U.M.A
Universidad de Zaragoza
Miguel Á. Marco Buzunáriz
Departamento de matemáticas – I.U.M.A.
Universidad de Zaragoza