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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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. Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated.
Other editions – View all Algebraic topology C. From Wikipedia, the free encyclopedia. This page was last edited on 11 Octoberat Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. 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.
Algebraic Topology – C. R. F. Maunder – Google Books
Homotopy and Simplicial Complexes. A simplicial complex is a topological space of a certain kind, constructed by “gluing together” pointsline segmentstrianglesand their n -dimensional counterparts see illustration. The translation process is usually carried out by means of the homology or homotopy groups of a topological space.
Fundamental groups and homology and cohomology groups are not only invariants of the underlying topological space, in the sense that two topological spaces which are homeomorphic have the same associated groups, but their associated morphisms also correspond — a continuous mapping of spaces induces a group homomorphism on the muander groups, and these homomorphisms can be used to show non-existence or, much more deeply, existence of mappings.
Algebraic topology – C. R. F. Maunder – Google Books
In homology a,gebraic and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. No eBook available Amazon.
Topolpgy translation process is usually carried out by means of the homology or homotopy groups of a topological space. Selected pages Title Page.
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.
The first and simplest homotopy group is the fundamental groupwhich records information about loops in a space.
Geomodeling Jean-Laurent Mallet Limited preview – Simplicial complexes should not be confused with the more qlgebraic notion of a simplicial set appearing in modern simplicial homotopy theory. Foundations of Combinatorial Topology. Courier Corporation- Mathematics – pages.
Wikimedia Commons has media related to Algebraic topology. The presentation of topoolgy homotopy theory and the account of duality in homology manifolds make the text ideal for a course on either homotopy or homology 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 for manifolds.
In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation of homeomorphism or more general homotopy of spaces. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. 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.
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.
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 alvebraic chains of homology theory. This was extended in the s, when Samuel Eilenberg and Norman Steenrod generalized this approach. 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.
They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms e. This class of spaces is broader and has some better categorical properties than simplicial complexesbut maumder retains a combinatorial nature that allows for computation often with a much smaller complex.
Read, highlight, and take notes, across web, tablet, and phone. The fundamental group of a finite simplicial complex does have a finite presentation.
Algebraic K-theory Exact sequence Glossary of algebraic manuder Grothendieck topology Higher category theory Higher-dimensional algebra Homological algebra.
In other projects Wikimedia Commons Wikiquote. One of the first mathematicians to work with different types of cohomology was Georges de Rham. Whitehead to meet the needs of homotopy theory.