Abstract
By an algebraic n-complex over Z[G] we mean an exact sequence of Z[G]-modules
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.
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Notes
- 1.
An interpretation of Yoneda product as composition in the derived module category is given in the thesis of Gollek [33].
References
Gollek, S.: Computations in the derived module category. Ph.D. Thesis, University College London (2010)
Johnson, F.E.A.: Stable Modules and the D(2)-Problem. LMS Lecture Notes in Mathematics, vol. 301. Cambridge University Press, Cambridge (2003)
Johnson, F.E.A.: Rigidity of hyperstable complexes. Arch. Math.. 90, 123–132 (2008)
MacLane, S.: Homology. Springer, Berlin (1963)
Whitehead, J.H.C.: Combinatorial homotopy II. Bull. Am. Math. Soc. 55, 453–496 (1949)
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Johnson, F.E.A. (2012). Classification of Algebraic Complexes. In: Syzygies and Homotopy Theory. Algebra and Applications, vol 17. Springer, London. https://doi.org/10.1007/978-1-4471-2294-4_8
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