Algebraic topology. Front Cover. C. R. F. Maunder. Van Nostrand Reinhold Co., – Mathematics Bibliographic information. QR code for Algebraic topology . Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic. Title, Algebraic Topology New university mathematics series · The @new mathematics series. Author, C. R. F. Maunder. Edition, reprint. Publisher, Van Nostrand.
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From Wikipedia, the free encyclopedia. Maunder Snippet view – The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope algdbraic they have a better chance of solution. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. The fundamental groups give us basic information about the algevraic of a topological space, but they are often nonabelian and can be difficult to work with.
They defined homology and cohomology as algrbraic equipped with natural transformations subject to certain axioms e. Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological algebra.
The author has given much attention to detail, yet ensures that the reader knows where he is going. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds.
No eBook available Amazon. A simplicial complex is a topological space of a certain kind, constructed by “gluing together” pointsline segments toplogy, trianglesand their n -dimensional counterparts see illustration. The presentation of the homotopy theory and the account of duality in homology manifolds K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Toology Topological quantum field theory.
In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation of homeomorphism or more general homotopy of spaces. Two major ways in which this can be done are through fundamental groupsor more generally homotopy theoryand through alvebraic and cohomology groups. Courier Corporation- Mathematics – pages. Much of the book is therefore concerned with the construction of these algebraic invariants, and with applications to topological problems, such as the classification of surfaces and duality theorems for manifolds.
The author has given much attention to detail, yet ensures that the reader knows where he is going. In less abstract language, cochains in the fundamental sense should assign ‘quantities’ to the chains of homology theory.
The fundamental group of a finite simplicial complex does have a finite presentation. The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology theory.
De Rham showed that all of these approaches were interrelated and that, for a closed, oriented manifold, the Betti numbers derived through simplicial homology were the same Betti numbers as those derived through de Rham cohomology.
Cohomology arises from the algebraic dualization of the construction of homology. In general, all constructions of algebraic topology are functorial ; the notions of categoryfunctor and natural transformation originated here.
Other editions – View all Algebraic topology C. Simplicial complex and CW complex. While inspired by knots that appear in daily life in shoelaces and rope, algenraic mathematician’s knot differs in that the ends are joined together so that it cannot be undone.
Examples include the planethe sphereand the toruswhich can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot be realized in three dimensions, but can be realized in four dimensions.
An older name for the subject was combinatorial topologyimplying an emphasis on how a space X was constructed from simpler ones  the modern standard tool for such construction is the CW complex. Selected pages Title Page. Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated. Whitehead topologh meet the needs of homotopy theory.
A CW complex is a type of topological space introduced by J. Homotopy and Simplicial Complexes.
The first and simplest homotopy group topoloyg the fundamental groupwhich records information about loops in a space. Homotopy Groups and CWComplexes. Whitehead Gordon Thomas Whyburn.
Read, highlight, and take notes, across web, tablet, and phone. Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory.
Retrieved from ” https: My library Help Advanced Book Search. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. The translation process is usually carried out by means of the homology or homotopy groups of a topological space.