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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For the topology of pointwise convergence, see Algebraic topology object. The basic goal is to find algebraic invariants algebrakc classify topological spaces up to homeomorphismthough usually most classify up to homotopy equivalence. Algebraic K-theory Exact sequence Glossary of algebraic topology Topplogy topology Higher category theory Higher-dimensional algebra Homological algebra.

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.

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. Algebraic topology is a branch of mathematics that uses tools mwunder abstract algebra to study topological spaces.

### Algebraic topology – Wikipedia

The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. Foundations of Combinatorial Topology. Other editions – View all Algebraic topology C. One of the first mathematicians to work with different types of cohomology was Georges de Rham.

Selected pages Title Page. 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.

Courier Corporation- Mathematics – pages. The first and simplest homotopy group is the fundamental groupwhich records information about loops in a space. They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms e. Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated.

The translation process is usually carried out by means of the homology or homotopy groups of a topological space. In other projects Wikimedia Commons Wikiquote. This page was last edited on 11 Octoberat 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.

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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. From Wikipedia, the free encyclopedia. Wikimedia Commons has media related to 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.

The translation process is usually carried out by means of the homology or homotopy groups of a topological space. A simplicial complex is a topological space of a certain kind, constructed by “gluing together” pointsline segmentstrianglesand their n -dimensional counterparts see illustration. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.

In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. Simplicial complex and CW complex. My library Help Advanced Book Search. 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. 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.

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

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. A CW complex is a type of topological space introduced by J. Whitehead Gordon Thomas Whyburn.

Geomodeling Jean-Laurent Mallet Limited preview – While inspired by knots that appear in daily life in shoelaces and rope, a mathematician’s knot differs in that the ends are joined together so that it cannot be undone.

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. That is, cohomology is defined as the abstract study of cochainscocyclesand coboundaries. Cohomology arises from the algebraic qlgebraic of mwunder construction of homology. Maunder Snippet view – In less abstract language, cochains in the fundamental sense should assign ‘quantities’ to the chains of homology theory.

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## Algebraic topology

Account Options Sign in. This was extended in the s, when Samuel Eilenberg and Norman Steenrod generalized this approach. Maunder Courier Corporation- Mathematics – pages 2 Reviews https: In general, all constructions of algebraic topology are functorial ; the notions of categoryfunctor and natural transformation originated here.

Cohomology and Duality Theorems. Two major ways in which this can be done are through fundamental groupsor more generally homotopy theoryand through homology and cohomology groups.

In homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. The fundamental group of a finite simplicial complex does have a finite presentation.