Vick, James W. Homology theory. An introduction to algebraic topology. 2. ed. (English) Zbl 0789.55004 Graduate Texts in Mathematics. 145. New York: Springer-Verlag. xiv, 242 p. (1994). The first edition of this textbook (1973; Zbl 0262.55005) dealt with singular homology. This second edition has an additional chapter on covering spaces, the fundamental group, and Van Kampen’s theorem. It also has an additional bibliography; both the old and new bibliographies are very extensive.Among the topics dealt with in the chapters on homology theory are the following: singular homology and cohomology with arbitrary coefficients; the Eilenberg-Steenrod axioms; cup, cap and cross products; PoincarĂ© and Lefschetz duality; fixed point theory.The book is very readable. It concentrates on the main ideas; the details of proofs are often left to the reader. Reviewer: R.J.Steiner (Glasgow) Cited in 2 ReviewsCited in 33 Documents MSC: 55N10 Singular homology and cohomology theory 55-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic topology Keywords:singular homology; covering spaces; fundamental group; Van Kampen’s theorem Citations:Zbl 0262.55005 PDF BibTeX XML Cite \textit{J. W. Vick}, Homology theory. An introduction to algebraic topology. 2. ed. New York: Springer-Verlag (1994; Zbl 0789.55004) OpenURL