Effective computation of degree bounded minimal models for GCDA's

TL;DR

This paper introduces a method for computing degree-bounded minimal models of finitely presented GCDAs, including an implementation and criteria for i-formality, advancing computational tools in algebraic topology.

Contribution

It presents a new generator-by-generator algorithm for minimal models of GCDAs, along with criteria for i-formality and a practical implementation.

Findings

Effective algorithm for minimal model computation.

Implementation demonstrating practical applicability.

Criteria for i-formality established.

Abstract

Given a finitely presented Graded Commutative Differential Algebra (GCDA), we present a method to compute its minimal model, together with a map that is a quasi-isomorphism up to a given degree. The method works by adding generators one by one. We also provide a specific implementation of the method. We also provide two criteria for i-formality, one necessary and one sufficient.