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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]
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 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.
110 Differential Algebraic Topology: From Stratifolds to Exotic Spheres, Matthias Kreck (2010, ISBN 978-0-8218-4898-2) 111 Ricci Flow and the Sphere Theorem, Simon Brendle (2010, ISBN 978-0-8218-4938-5) 112 Optimal Control of Partial Differential Equations: Theory, Methods and Applications, Fredi Troltzsch (2010, ISBN 978-0-8218-4904-0)
Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces The main article for this category is Algebraic topology . Contents
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 ...
In mathematics, nonabelian algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras.. Many of the higher-dimensional algebraic structures are noncommutative and, therefore, their study is a very significant part of nonabelian category theory, and also of Nonabelian Algebraic Topology (NAAT), [1] which generalises to higher ...
While this concept is too strict for some purposes in for example, homotopy theory, where "weak" structures arise in the form of higher categories, [2] strict cubical higher homotopy groupoids have also arisen as giving a new foundation for algebraic topology on the border between homology and homotopy theory; see the article Nonabelian ...