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2. Grothendieck's Galois theory - Wikipedia

   en.wikipedia.org/wiki/Grothendieck's_Galois_theory

   It provides, in the classical setting of field theory, an alternative perspective to that of Emil Artin based on linear algebra, which became standard from about the 1930s. The approach of Alexander Grothendieck is concerned with the category-theoretic properties that characterise the categories of finite G -sets for a fixed profinite group G .

3. Lehrbuch der Topologie - Wikipedia

   en.wikipedia.org/wiki/Lehrbuch_der_Topologie

   In mathematics, Lehrbuch der Topologie (German for "textbook of topology") is a book by Herbert Seifert and William Threlfall, first published in 1934 and published in an English translation in 1980. It was one of the earliest textbooks on algebraic topology, and was the standard reference on this topic for many years. Albert W. Tucker wrote a ...

4. 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 ...

5. Pushout (category theory) - Wikipedia

   en.wikipedia.org/wiki/Pushout_(category_theory)

   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 ...

6. A Guide to the Classification Theorem for Compact Surfaces

   en.wikipedia.org/wiki/A_Guide_to_the...

   Readers of the book are expected to already be familiar with general topology, linear algebra, and group theory. [1] However, as a textbook, it lacks exercises, and reviewer Bill Wood suggests its use for a student project rather than for a formal course. [1] Many other graduate algebraic topology textbooks include coverage of the same topic. [4]

7. Eilenberg–MacLane space - Wikipedia

   en.wikipedia.org/wiki/Eilenberg–MacLane_space

   In mathematics, specifically algebraic topology, an Eilenberg–MacLane space [note 1] is a topological space with a single nontrivial homotopy group. Let G be a group and n a positive integer . A connected topological space X is called an Eilenberg–MacLane space of type K ( G , n ) {\displaystyle K(G,n)} , if it has n -th homotopy group π n ...

8. 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 ...

9. Todd class - Wikipedia

   en.wikipedia.org/wiki/Todd_class

   In mathematics, the Todd class is a certain construction now considered a part of the theory in algebraic topology of characteristic classes.The Todd class of a vector bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notably in differential topology, the theory of complex manifolds and algebraic geometry.