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A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999. x+243 pp. ISBN 0-226-51182-0, 0-226-51183-9; Edwin H. Spanier. Algebraic topology. Corrected reprint of the 1966 original. Springer-Verlag, New York-Berlin, 1981. xvi+528 pp. ISBN 0-387-90646-0; George W. Whitehead. Elements ...
An Introduction to Homological Algebra (1979), Pure and Applied Mathematics, vol. 85, Academic Press; ISBN 0-12-599250-5 [7] An Introduction to Algebraic Topology (1988), Springer-Verlag; ISBN 0-387-96678-1; An Introduction to the Theory of Groups (1995), Springer-Verlag; ISBN 0-387-94285-8
Albrecht Dold: Lectures on Algebraic Topology, Springer ISBN 3-540-58660-1. Allen Hatcher: Algebraic Topology, Cambridge University Press ISBN 978-0-521-79540-1. A free electronic version is available on the author's homepage
A torus, one of the most frequently studied objects in algebraic topology. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
In mathematics, more specifically algebraic topology, a pair (,) is shorthand for an inclusion of topological spaces:.Sometimes is assumed to be a cofibration.A morphism from (,) to (′, ′) is given by two maps : ′ and : ′ such that ′ =.
A Concise Course in Algebraic Topology. University of Chicago Press. pp. 183– 198. ISBN 0-226-51182-0. This textbook gives a detailed construction of the Thom class for trivial vector bundles, and also formulates the theorem in case of arbitrary vector bundles. Stong, Robert E. (1968). Notes on cobordism theory. Princeton University Press ...
Differential graded algebra: the algebraic structure arising on the cochain level for the cup product; Poincaré duality: swaps some of these; Intersection theory: for a similar theory in algebraic geometry
Among his several books and standard topology and algebraic topology textbooks are: Elements of Modern Topology (1968), Low-Dimensional Topology (1979, co-edited with T.L. Thickstun), Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid (1998), [15] [16] Topology and Groupoids (2006) [17] and ...