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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A simplicial complex is a topological space of a certain kind, constructed by “gluing together” points munder, line segmentstrianglesand their n -dimensional counterparts see illustration. My library Help Advanced Book Search. They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms e.
Simplicial complexes should not be confused with the more abstract notion of a,gebraic simplicial set appearing in modern simplicial homotopy theory. Whitehead to meet the needs of homotopy theory. 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.
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.
One of the first mathematicians to work with different types of cohomology algebrai Georges de Rham. Introduction to Knot Theory. 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.
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. 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. Maunder has provided many alegbraic 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.
Algebraic topology – Wikipedia
Retrieved from ” https: The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated.
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. K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Sheaf Toopology quantum field theory.
Maunder Snippet view – Topologj Courier Corporation- Mathematics – pages 2 Reviews https: In the s and s, there was growing emphasis on investigating topological spaces by finding correspondences from them to algebraic groupswhich led to the change of name topollgy algebraic topology.
Courier Corporation- Mathematics – pages. The presentation of the homotopy theory and the account of duality in homology manifolds Other editions – View all Algebraic topology C.
Algebraic Topology – C. R. F. Maunder – Google Books
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. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.
Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Wikimedia Commons has media related to Algebraic topology. A manifold is a topological space that near each point resembles Euclidean space. 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. This page was last edited on 11 Octoberat Simplicial complex and CW complex.
Homotopy and Simplicial Complexes. maundder
That is, cohomology is defined as the abstract study of cochainscocyclesand coboundaries. Views Read Edit View history.