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Classification of Algebraic Complexes

  • F. E. A. JohnsonEmail author
Chapter
  • 935 Downloads
Part of the Algebra and Applications book series (AA, volume 17)

Abstract

By an algebraic n-complex over Z[G] we mean an exact sequence of Z[G]-modules
$$E_* = (0 \rightarrow J \rightarrow E_n \stackrel{\partial_n}{\rightarrow} E_{n-1} \stackrel{\partial _{n-1}}{\rightarrow} \cdots\stackrel{\partial_2}{\rightarrow}E_1 \stackrel{\partial_1}{\rightarrow} E_0\rightarrow\mathbf{ Z} \rightarrow0)$$
in which each E r is finitely generated and stably free over Z[G]. The notion is an abstraction from a cell complex X with π 1(X)=G for which \(\pi_{r}(\tilde{X}) = 0\) for 0<r<n. In this chapter we use the Swan homomorphism of Chap.  7 to classify algebraic n-complexes up to homotopy equivalence.

Keywords

Algebraic Complexity Swan Homomorphism Weak Homotopy Equivalence Exact Sequence Yoneda Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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