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In algebraic topology, the Betti numbers are used to distinguish ... sequence of non-zero Betti numbers. An example is the infinite ... ISBN 0-387-90894-3. Roe ...
Higher category theory is often applied in algebraic topology ... An example in topology is the composition of paths, ... ISBN 978-0-691-14048-3. ...
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.
It has applications in nonabelian algebraic topology, ... as for example in the case of a gauge theory, ... ISBN 978-3-03719-083-8. ...
The original approach to Chern classes was via algebraic topology: ... a Chern number of the vector bundle. For example, ... ISBN 978-3-662-02421-8. ...
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
Homotopy; Path (topology) Fundamental group; Homotopy group; Seifert–van Kampen theorem; Pointed space; Winding number; Simply connected. Universal cover; Monodromy
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 ′ =.