Freeness conditions for crossed squares and squared complexes

MUTLU A., Porter T.

K-Theory, vol.20, no.4, pp.345-368, 2000 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2000
  • Doi Number: 10.1023/a:1026535602325
  • Journal Name: K-Theory
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.345-368
  • Keywords: crossed square, squared complex, free simplicial group
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Following Ellis, we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, in terms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely algebraic derivation of a result of Brown and Loday.