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2. Algebraic topology - Wikipedia

   en.wikipedia.org/wiki/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 .

3. Topological algebra - Wikipedia

   en.wikipedia.org/wiki/Topological_algebra

   A topological algebra over a topological field is a topological vector space together with a bilinear multiplication ⋅ : A × A → A {\displaystyle \cdot :A\times A\to A} , ( a , b ) ↦ a ⋅ b {\displaystyle (a,b)\mapsto a\cdot b}

4. Torsor (algebraic geometry) - Wikipedia

   en.wikipedia.org/wiki/Torsor_(algebraic_geometry)

   Let be a Grothendieck topology and a scheme.Moreover let be a group scheme over , a -torsor (or principal -bundle) over for the topology (or simply a -torsor when the topology is clear from the context) is the data of a scheme and a morphism : with a -invariant (right) action on that is locally trivial in i.e. there exists a covering {} such that the base change over is isomorphic to the ...

5. Category:Algebraic topology - Wikipedia

   en.wikipedia.org/wiki/Category:Algebraic_topology

   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 ...

6. List of algebraic topology topics - Wikipedia

   en.wikipedia.org/wiki/List_of_algebraic_topology...

   Chain (algebraic topology) Betti number; Euler characteristic. Genus; Riemann–Hurwitz formula; Singular homology; Cellular homology; Relative homology; Mayer–Vietoris sequence; Excision theorem; Universal coefficient theorem; Cohomology. List of cohomology theories; Cocycle class; Cup product; Cohomology ring; De Rham cohomology; Čech ...

7. Algebraic topology (object) - Wikipedia

   en.wikipedia.org/wiki/Algebraic_topology_(object)

   This terminology is often used in the case of the algebraic topology on the set of discrete, faithful representations of a Kleinian group into PSL(2,C). Another topology, the geometric topology (also called the Chabauty topology ), can be put on the set of images of the representations, and its closure can include extra Kleinian groups that are ...

8. Directed algebraic topology - Wikipedia

   en.wikipedia.org/wiki/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 .

9. Chain (algebraic topology) - Wikipedia

   en.wikipedia.org/wiki/Chain_(algebraic_topology)

   In algebraic topology, a k-chain is a formal linear combination of the k-cells in a cell complex. In simplicial complexes (respectively, cubical complexes ), k -chains are combinations of k -simplices (respectively, k -cubes), [ 1 ] [ 2 ] [ 3 ] but not necessarily connected.