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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 ...
Allen Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, 2002. ISBN 0-521-79540-0. A modern, geometrically flavored introduction to algebraic topology. The book is available free in PDF and PostScript formats on the author's homepage. Kainen, P. C. (1971). "Weak Adjoint Functors". Mathematische Zeitschrift. 122: 1– 9.
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 ...
The topology on X an is called the "complex topology" (and is very different from the subspace topology). Suppose φ: X → Y is a morphism of schemes of locally finite type over C. Then there exists a continuous map φ an: X an → Y an such that λ Y ∘ φ an = φ ∘ λ X.
The universal enveloping algebra of a graded Lie algebra L is the quotient of the tensor algebra of L by the two-sided ideal generated by all elements of the form () | | | | [,]. In algebraic topology , the term usually refers to the corollary of the aforementioned result, that for a pointed , simply connected space X , the following ...
A 1 homotopy theory is founded on a category called the A 1 homotopy category ().Simply put, the A 1 homotopy category, or rather the canonical functor (), is the universal functor from the category of smooth -schemes towards an infinity category which satisfies Nisnevich descent, such that the affine line A 1 becomes contractible.
In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander Grothendieck. The early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch.
Tammo tom Dieck 1972. Tammo tom Dieck (29 May 1938, São Paulo) is a German mathematician, specializing in algebraic topology.. Tammo tom Dieck studied mathematics from 1957 at the University of Göttingen and at Saarland University, where he received his promotion (Ph.D.) in 1964 under Dieter Puppe with thesis Zur -Theorie und ihren Kohomologie-Operationen. [1]