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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 ...
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 ...
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}
An introduction to categorical approaches to algebraic topology: the focus is on the algebra, and assumes a topological background. Ronald Brown "Topology and Groupoids" pdf available Gives an account of some categorical methods in topology, use the fundamental groupoid on a set of base points to give a generalisation of the Seifert-van Kampen ...
Differential graded algebra: the algebraic structure arising on the cochain level for the cup product; Poincaré duality: swaps some of these; Intersection theory: for a similar theory in algebraic geometry
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they ...
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Jon Peter May (born September 16, 1939, in New York) is an American mathematician working in the fields of algebraic topology, category theory, homotopy theory, and the foundational aspects of spectra. He is known, in particular, for the May spectral sequence and for coining the term operad.