Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

On constructing resolutions over the polynomial

Pages: 315 – 336

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n2.a15

Authors

Leif Johansson (Mathematics Department, Stockholm University, Sweden)

Larry Lambe (School of Informatics, Division of Mathematics, University of Wales, Bangor, Gwynedd, Wales, United Kingdom)

Emil Sköldberg (Mathematics Department, Stockholm University, Sweden)

Abstract

Let $k$ be a field, and $A$ be a polynomial algebra over $k$. Let $I\subseteq A$ be an ideal. We present a novel method for computing resolutions of $A/I$ over $A$. The method is a synthesis of Gröbner basis techniques and homological perturbation theory. The examples in this paper were computed using computer algebra.

Keywords

homology, homotopy, homological perturbation, resolution, polynomial ring, Gröbner basis, normal form

2010 Mathematics Subject Classification

13D02

Full Text (PDF format)