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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]
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 ...
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 .
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]
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 ...
In mathematics, specifically algebraic topology, the mapping cylinder [1] of a continuous function between topological spaces and is the quotient = (([,])) / where the denotes the disjoint union, and ~ is the equivalence relation generated by
Let be a Grothendieck topology and a scheme.Moreover let be a group scheme over , a -torsor (or principal -bundle) over for the topology (or simply a -torsor when the topology is clear from the context) is the data of a scheme and a morphism : with a -invariant (right) action on that is locally trivial in i.e. there exists a covering {} such that the base change over is isomorphic to the ...
There is a closely related argument from algebraic topology, using the Lefschetz fixed-point theorem. Since the Betti numbers of a 2-sphere are 1, 0, 1, 0, 0, ... the Lefschetz number (total trace on homology ) of the identity mapping is 2.