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An Invitation to Computational Homotopy$
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Graham Ellis

Print publication date: 2019

Print ISBN-13: 9780198832973

Published to Oxford Scholarship Online: November 2019

DOI: 10.1093/oso/9780198832973.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 September 2021

Cohomology of Homotopy 2-types

Cohomology of Homotopy 2-types

Chapter:
(p.379) 5 Cohomology of Homotopy 2-types
Source:
An Invitation to Computational Homotopy
Author(s):

Graham Ellis

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198832973.003.0005

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: the fundamental crossed modules of a CW-complex, cat-1-groups, simplicial groups, Moore complexes, the Dold-Kan correspondence, integral homology of simplicial groups, homological perturbation theory. A manual classification of homotopy classes of maps from a surface to the projective plane is also included.

Keywords:   computational algebra, crossed module, simplicial group, homology, homological perturbation, homotopy 2-type, homotopy group, homotopy classification, projective plane, Dold-Kan theorem

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