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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.
In mathematics, Lehrbuch der Topologie (German for "textbook of topology") is a book by Herbert Seifert and William Threlfall, first published in 1934 and published in an English translation in 1980. It was one of the earliest textbooks on algebraic topology, and was the standard reference on this topic for many years. Albert W. Tucker wrote a ...
Singular cohomology is a powerful invariant in topology, associating a graded-commutative ring with any topological space. Every continuous map: determines a homomorphism from the cohomology ring of to that of ; this puts strong restrictions on the possible maps from to .
This terminology is often used in the case of the algebraic topology on the set of discrete, faithful representations of a Kleinian group into PSL(2,C). Another topology, the geometric topology (also called the Chabauty topology ), can be put on the set of images of the representations, and its closure can include extra Kleinian groups that are ...
The Godement resolution of a sheaf is a construction in homological algebra that allows one to view global, cohomological information about the sheaf in terms of local information coming from its stalks.
In the simplest possible case the relationship is that of a tensor product, but for applications it is very often necessary to apply certain tools of homological algebra to express the answer. A Künneth theorem or Künneth formula is true in many different homology and cohomology theories, and the name has become generic.
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
The barycentric subdivision is an operation on simplicial complexes. In algebraic topology it is sometimes useful to replace the original spaces with simplicial complexes via triangulations: The substitution allows to assign combinatorial invariants as the Euler characteristic to the spaces.