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He was known for his book on non-Euclidean geometry (1st edition, 1974; 4th edition, 2008) [3] [4] and his book on algebraic topology (1st edition, 1967, published with the title Lectures on Algebraic Topology; revised edition published, with John R. Harper as co-author, in 1981 with the title Algebraic Topology: A First Course). [5] [6] [7]
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 ...
A mapping : between total spaces of two fibrations : and : with the same base space is a fibration homomorphism if the following diagram commutes: . The mapping is a fiber homotopy equivalence if in addition a fibration homomorphism : exists, such that the mappings and are homotopic, by fibration homomorphisms, to the identities and . [2]: 405-406
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 ...
However, in 2012 Bourbaki resumed publication of the Éléments with a revised and expanded edition of the eighth chapter of Algebra, the first of new books on algebraic topology (covering also material that had originally been planned as the eleventh chapter of the group's book on general topology) [11] and the two volumes of significantly ...
Totaro participated in the Study of Mathematically Precocious Youth while in grade school and enrolled at Princeton University in 1980 at the age of thirteen, becoming the youngest freshman in its history. [1] He scored a perfect 800 on the math portion and a 690 on the verbal portion of the SAT-I exam at the age of 12. [1]
The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. This is a list of topology topics. See also: Topology glossary; List of topologies; List of general topology topics; List of geometric topology topics
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 ...