Search for "Algebraic topology" in article titles:

1. 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. (Branch of mathematics) [100%] 2023-11-05 [Algebraic topology]
2. Algebraic topology: The branch of mathematics in which one studies such properties of geometrical figures (in a wider sense, of all objects for which one can speak of continuity), and their mappings into each other, which remain unchanged under continuous deformations (homotopies ... (Mathematics) [100%] 2023-10-28
3. 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. (Branch of mathematics) [100%] 2023-06-07 [Algebraic topology]
4. Algebraic topology: Algebraic topology is a branch of mathematics that uses abstract algebra to understand topological spaces, and topology to understand abstract algebra. The primary method of algebraic topology is to identify some kind of relation between a group (or a ring ... [100%] 2023-02-22 [Topology] [Algebra]...
5. Algebraic topology (object): In mathematics, the algebraic topology on the set of group representations from G to a topological group H is the topology of pointwise convergence, i.e. pi converges to p if the limit of pi(g) = p(g) for every ... (Object) [81%] 2023-04-11 [3-manifolds] [Algebraic topology]...
6. Algebraic topology based on knots: A branch of mathematics on the border of topology (cf. also Topology, general) and algebra, in which one analyzes properties of manifolds by considering links (submanifolds) in a manifold and their algebraic structure (cf. (Mathematics) [63%] 2023-07-01
7. Directed algebraic topology: In mathematics, directed algebraic topology is a refinement of algebraic topology for directed spaces, topological spaces and their combinatorial counterparts equipped with some notion of direction. Some common examples of directed spaces are spacetimes and simplicial sets. [81%] 2023-12-27 [Algebraic topology]
8. Quantum Algebraic Topology: Quantum Algebraic Topology is a theoretical subfield of quantum physics focused on quantum operator algebra and topology of quantum spaces. Both topological quantum field theory and noncommutative geometry may be considered related fields. [81%] 2023-03-03 [Topology]
9. Nonabelian algebraic topology: 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 ... [81%] 2024-06-23 [Algebraic topology]
10. Path space (algebraic topology): In algebraic topology, a branch of mathematics, the path space \displaystyle{ PX }[/math] of a based space \displaystyle{ (X, *) }[/math] is the space that consists of all maps \displaystyle{ f }[/math] from the interval \displaystyle{ I = [0, 1] }[/math] to ... (Algebraic topology) [70%] 2023-01-03 [Algebraic topology] [Mathematics]...
11. Good cover (algebraic topology): In mathematics, an open cover of a topological space \displaystyle{ X }[/math] is a family of open subsets such that \displaystyle{ X }[/math] is the union of all of the open sets. A good cover is an open cover in ... (Algebraic topology) [70%] 2024-03-21 [Algebraic topology] [Cohomology theories]...