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Allen Hatcher, On the boundary curves of incompressible surfaces, Pacific Journal of Mathematics 99 (1982), no. 2, 373–377. William Floyd and Allen Hatcher, Incompressible surfaces in punctured-torus bundles, Topology and its Applications 13 (1982), no. 3, 263–282. Allen Hatcher and William Thurston, Incompressible surfaces in 2-bridge knot ...
Allen Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, 2002. ISBN 0-521-79540-0. A modern, geometrically flavored introduction to algebraic topology. The book is available free in PDF and PostScript formats on the author's homepage. Kainen, P. C. (1971). "Weak Adjoint Functors". Mathematische Zeitschrift. 122: 1–9.
Hatcher, Allen (2002), Algebraic Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0. A modern, geometrically flavoured introduction to algebraic topology. Higgins, Philip J. (1971), Notes on categories and groupoids, Van Nostrand Reinhold, ISBN 9780442034061
Allen Hatcher, Algebraic topology. Cambridge University Press, ISBN 0-521-79160-X and ISBN 0-521-79540-0; J.P. May, A Concise Course in Algebraic Topology, Chicago University Press ISBN 0-226-51183-9; Joseph J. Rotman, An Introduction to Algebraic Topology, Springer-Verlag, ISBN 0-387-96678-1
In algebraic topology, the pushforward of a continuous function : between two topological spaces is a homomorphism: () between the homology groups for . Homology is a functor which converts a topological space X {\displaystyle X} into a sequence of homology groups H n ( X ) {\displaystyle H_{n}\left(X\right)} .
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group , denoted π 1 ( X ) , {\displaystyle \pi _{1}(X),} which records information about loops in a space .
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
The Serre spectral sequence is covered in most textbooks on algebraic topology, e.g. Allen Hatcher, Spectral Sequences; Edwin Spanier, Algebraic topology, Springer; Also James Davis, Paul Kirk, Lecture notes in algebraic topology gives many nice applications of the Serre spectral sequence. An elegant construction is due to
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