Search results
Results from the WOW.Com Content Network
A topological algebra over a topological field is a topological vector space together with a bilinear multiplication ⋅ : A × A → A {\displaystyle \cdot :A\times A\to A} , ( a , b ) ↦ a ⋅ b {\displaystyle (a,b)\mapsto a\cdot b}
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.
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 .
edit] * The base point of a based space. X + {\displaystyle X_{+}} For an unbased space X, X + is the based space obtained by adjoining a disjoint base point. A absolute neighborhood retract abstract 1. Abstract homotopy theory Adams 1. John Frank Adams. 2. The Adams spectral sequence. 3. The Adams conjecture. 4. The Adams e -invariant. 5. The Adams operations. Alexander duality Alexander ...
Albrecht Dold: Lectures on Algebraic Topology, Springer ISBN 3-540-58660-1. Allen Hatcher: Algebraic Topology, Cambridge University Press ISBN 978-0-521-79540-1. A free electronic version is available on the author's homepage
A Concise Course in Algebraic Topology. University of Chicago Press. pp. 183– 198. ISBN 0-226-51182-0. This textbook gives a detailed construction of the Thom class for trivial vector bundles, and also formulates the theorem in case of arbitrary vector bundles. Stong, Robert E. (1968). Notes on cobordism theory. Princeton University Press ...
Example of singular 1-chains: The violet and orange 1-chains cannot be realized as a boundary of a 2-chain. The usual construction of singular homology proceeds by defining formal sums of simplices, which may be understood to be elements of a free abelian group, and then showing that we can define a certain group, the homology group of the topological space, involving the boundary operator.
For example, a sphere has two cells: one 0-cell and one -cell, since can be obtained by collapsing the boundary of the n-disk to a point. In general, every manifold has the homotopy type of a CW complex; [ 3 ] in fact, Morse theory implies that a compact manifold has the homotopy type of a finite CW complex.