The Cockcroft–Swan theorem is proved for n-dimensional projective crossed chain complexes (Pi,G, ∂ i ), where G = A * F is a free product of a fixed group A by a free finitely generated group F.
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W. Cockcroft and R. Swan, “On the homotopy type of certain two-dimensional complexes,” Proc. London Math. Soc., 11, 193–202 (1961).
N. A. Khmel’nitskii, “On the chain equivalence of projective chain complexes,” Ukr. Math. J., 64, Issue 6, 948–957 (2012).
V. V. Sharko, Functions on Manifolds: Algebraic and Topological Aspects, American Mathematical Society, Providence, R.I. (1993).
R. Brown, P. J. Higgins, and R. Sivera, Nonabelian Algebraic Topology, European Mathematical Society, Zürich (2011).
J. H. C. Whitehead, “Combinatorial homotopy,” Bull. Amer. Math. Soc., 55, No. 4, 453–496 (1949).
J. Ratcliffe, “Free and projective modules,” J. London Math. Soc., 22, No. 1, 66–74 (1980).
J. Ratcliffe, “On complexes dominated by a two-complex,” Combinatorial Group Theory and Topology, Ann. Math. Studies, 111, 221–254 (1986).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 12, pp. 1694–1704, December, 2014.
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Khmel’nitskii, N.A. Cockcroft–Swan Theorem for Projective Crossed Chain Complexes. Ukr Math J 66, 1904–1916 (2015). https://doi.org/10.1007/s11253-015-1058-4
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DOI: https://doi.org/10.1007/s11253-015-1058-4