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Allen Hatcher and William Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980), no. 3, 221–237. Allen Hatcher, On the boundary curves of incompressible surfaces, Pacific Journal of Mathematics 99 (1982), no. 2, 373–377.
In algebraic topology, singular homology refers to the study of a certain set of algebraic invariants of a topological space, the so-called homology groups (). Intuitively, singular homology counts, for each dimension , the -dimensional holes of a space.
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. Although algebraic topology primarily uses algebra to study topological ...
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.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
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
Hatcher, Allen (2002), Algebraic Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0. Jean-Pierre Marquis (2006) "A path to Epistemology of Mathematics: Homotopy theory", pages 239 to 260 in The Architecture of Modern Mathematics, J. Ferreiros & J.J. Gray, editors, Oxford University Press ISBN 978-0-19-856793-6
Topology and geometry, Graduate Texts in Mathematics, Springer Verlag 1993, 1996; Davis, Donald. "Table of immersions and embeddings of real projective spaces" Hatcher, Allen (2001). Algebraic Topology. Cambridge University Press. ISBN 978-0-521-79160-1
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