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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. Although algebraic topology primarily uses algebra to study topological ...

  3. Intersection theory - Wikipedia

    en.wikipedia.org/wiki/Intersection_theory

    William Fulton in Intersection Theory (1984) writes ... if A and B are subvarieties of a non-singular variety X, the intersection product A · B should be an equivalence class of algebraic cycles closely related to the geometry of how A ∩ B, A and B are situated in X. Two extreme cases have been most familiar.

  4. Glossary of algebraic topology - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_algebraic_topology

    This is a glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory, glossary of differential geometry and topology, Timeline of manifolds. Convention: Throughout the article, I denotes the unit interval, S n the n-sphere and D n the n ...

  5. William Fulton (mathematician) - Wikipedia

    en.wikipedia.org/wiki/William_Fulton_(mathematician)

    In 1996 he received the Steele Prize for mathematical exposition for his text Intersection Theory. [1] Fulton is a member of the United States National Academy of Sciences since 1997; a fellow of the American Academy of Arts and Sciences from 1998, and was elected a foreign member of the Royal Swedish Academy of Sciences in 2000. [3]

  6. 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 ...

  7. Euler characteristic - Wikipedia

    en.wikipedia.org/wiki/Euler_characteristic

    In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

  8. Chern class - Wikipedia

    en.wikipedia.org/wiki/Chern_class

    There are various ways of approaching the subject, each of which focuses on a slightly different flavor of Chern class. The original approach to Chern classes was via algebraic topology: the Chern classes arise via homotopy theory which provides a mapping associated with a vector bundle to a classifying space (an infinite Grassmannian in this case).

  9. Fundamental group - Wikipedia

    en.wikipedia.org/wiki/Fundamental_group

    In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space.