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 ยท The @new mathematics series. Author, C. R. F. Maunder. Edition, reprint. Publisher, Van Nostrand.

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The presentation of the homotopy theory and the account of duality in homology manifolds Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.

Cohomology and Duality Theorems. Retrieved from ” https: The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Examples include the planethe maundderand 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.

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 algfbraic Rham cohomology. One of the first mathematicians to work with different types of cohomology was Georges de Rham. While inspired by knots that appear in daily life in shoelaces algebrwic rope, a topoloty knot differs in that the ends are joined together so that it cannot be undone.

Account Options Sign in. An older name for the subject was combinatorial topologyimplying an emphasis on how a space X was constructed from simpler ones [2] the modern standard tool for such construction is the CW complex.

The author has given much attention to detail, yet ensures that the reader knows where he is going. Whitehead Gordon Thomas Whyburn.

### Algebraic Topology

A CW complex is a type of topological space introduced by J. Maunder has provided many examples and exercises as an aid, and the notes and references at the end of each chapter trace the historical development of the subject and also point the way to more advanced results.

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. The author has given much attention to detail, yet ensures that the reader knows where he is going.

Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.

Views Read Edit View history. Other editions – View all Algebraic topology C. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphismthough usually most classify up to homotopy equivalence. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does maunrer.

The fundamental groups give us basic information about the structure of a topological space, but they are often nonabelian and can be difficult to work with. Whitehead to meet the needs of homotopy theory. By using this site, you agree to the Terms of Use and Privacy Policy.

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. The translation process is usually carried out by means of the homology or homotopy groups of a topological space. Geomodeling Jean-Laurent Mallet Limited preview – The idea of algebraic topology is to translate problems in topology into problems in algebra with the hope that they have a better chance of solution.

K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Sheaf Topological quantum field theory.

### Algebraic Topology – C. R. F. Maunder – Google Books

Finitely generated abelian groups are completely classified and are particularly easy to work with. Simplicial complex and CW complex. They defined homology and cohomology as functors 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 K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Sheaf Topological quantum field theory.

## Algebraic topology

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.

In the algevraic approach, one finds a correspondence algebdaic spaces and groups that respects the relation of homeomorphism or more general homotopy of spaces. Product Description Product Details Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint.

Introduction to Knot Theory. Maunder Courier Corporation- Mathematics – pages 2 Reviews https: Foundations of Combinatorial Topology.

## Algebraic Topology

The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal qlgebraic a course on either homotopy or homology theory. In general, all constructions of algebraic topology are functorial ; the notions of categoryfunctor and natural transformation originated here.

Courier Corporation- Mathematics – pages. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. From Wikipedia, the free encyclopedia. Algebraci was extended in the s, when Samuel Eilenberg and Norman Steenrod generalized this approach. For the topology of pointwise convergence, see Algebraic topology object. Cohomology arises from the algebraic dualization of the construction of homology.