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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This class of spaces is broader and has some better categorical properties than simplicial complexesbut still retains a combinatorial nature that allows for computation often with a much smaller complex.

Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated. Homotopy and Simplicial Complexes. The translation process is usually carried out by means algeraic the homology or homotopy groups of a topological space.

### Algebraic Topology

Examples include the planethe sphereand the toruswhich can all be realized in three dimensions, but also the Klein bottle and real projective plane which tppology be realized in three dimensions, topokogy can be realized in four dimensions.

Two major ways in which this can be done are through fundamental groupsor more generally homotopy theoryand through homology and cohomology groups. Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological algebra.

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

## Algebraic topology

This page was last edited on 11 Algebrajcat This allows one to recast statements about topological spaces into statements about groups, which have a great deal of manageable structure, often making these statement easier to prove. In homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex.

Retrieved from ” https: The translation process is usually carried out by means of the homology or homotopy groups of a topological space. The purely combinatorial counterpart to a simplicial complex is algevraic abstract simplicial complex. That is, cohomology is defined as the abstract study of cochainscocyclesand coboundaries. Whitehead to meet the needs of homotopy theory. 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 algebraiic manifolds.

Read, highlight, and take notes, across web, tablet, and phone. Foundations of Combinatorial Topology.

The presentation of the homotopy theory and the account of duality in homology manifolds The fundamental group of a finite simplicial complex does have a finite presentation. Account Options Sign in.

## Algebraic Topology

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 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. Wikimedia Commons has media related to Algebraic topology.

By using this site, you agree to the Terms of Use and Privacy Policy. Geomodeling Jean-Laurent Mallet Limited preview – 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.

In general, all constructions of algebraic topology are functorial ; the notions of categoryfunctor and natural transformation originated here.

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 is a branch of mathematics that uses tools from abstract algebra to study topological spaces. 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.

A manifold is a topological space that near each point resembles Euclidean space. Simplicial complex and CW complex. No eBook available Amazon. 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.

A CW complex is a type of topological space introduced by J. Selected pages Title Page. Cohomology Operations and Applications in Homotopy 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.

Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology.

In other projects Wikimedia Commons Wikiquote. Introduction to Knot Theory. 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. Views Read Edit View history. Maunder Courier Corporation- Mathematics – pages 2 Reviews https: Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory.

Homotopy Groups and CWComplexes. 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 algebrraic for manifolds.