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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 .
In the above example, a connection with classical Galois theory can be seen by regarding ^ as the profinite Galois group Gal(F /F) of the algebraic closure F of any finite field F, over F. That is, the automorphisms of F fixing F are described by the inverse limit, as we take larger and larger finite splitting fields over F .
Call a cohomology theory even periodic if = for i odd and there is an invertible element .These theories possess a complex orientation, which gives a formal group law.A particularly rich source for formal group laws are elliptic curves.
Massey, William S. (1991), A Basic Course in Algebraic Topology, Springer, ISBN 038797430X; May, J. Peter (1999), A Concise Course in Algebraic Topology, ISBN 9780226511832; Deane Montgomery and Leo Zippin, Topological Transformation Groups, Interscience Publishers (1955) Munkres, James R. (2000), Topology, Prentice Hall, ISBN 0-13-181629-2
In mathematics, the Hurewicz theorem is a basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism. The theorem is named after Witold Hurewicz , and generalizes earlier results of Henri Poincaré .
Since 2002 Cohen has been one of the developers and contributors to the theory of String topology, which was introduced originally by Moira Chas and Dennis Sullivan. In 1995, Cohen was a founder of the Stanford University Math Camp (SUMaC), a summer camp for mathematically talented high school students.
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).
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 ...