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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 ...
He was known for his book on non-Euclidean geometry (1st edition, 1974; 4th edition, 2008) [3] [4] and his book on algebraic topology (1st edition, 1967, published with the title Lectures on Algebraic Topology; revised edition published, with John R. Harper as co-author, in 1981 with the title Algebraic Topology: A First Course). [5] [6] [7]
Fundamental groups also appear in algebraic geometry and are the main topic of Alexander Grothendieck's first Séminaire de géométrie algébrique (SGA1). A version of Van Kampen's theorem appears there, and is proved along quite different lines than in algebraic topology, namely by descent theory. A similar proof works in algebraic topology. [18]
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 ...
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 A First Course in Abstract Algebra (2000), Prentice Hall; ISBN 0-13-011584-3
A First Course in Modular Forms, Fred Diamond, J. Shurman, (2006, ISBN 978-0-387-23229-4) The Geometry of Syzygies – A Second Course in Algebraic Geometry and Commutative Algebra, David Eisenbud (2005, ISBN 978-0-387-22215-8) An Introduction to Markov Processes, Daniel W. Stroock, (2014, 2nd ed., ISBN 978-3-540-23499-9)
Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces Subcategories. This category has the following ...
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 ...
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