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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Geomodeling Jean-Laurent Mallet Limited preview – This page was last edited on 11 Octoberat 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. K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Sheaf Topological quantum field 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. Read, highlight, and take notes, across web, tablet, and phone.
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.
Courier Corporation- Mathematics – pages. 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.
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Knot theory is the study of mathematical knots. My library Help Advanced Book Search. Selected pages Title Page. The author has given much attention to detail, yet ensures that the reader knows where he is algebrxic.
The presentation of the homotopy theory and the account of duality in homology manifolds make the text ideal for a course on topolofy homotopy or homology theory.
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.
Cohomology Operations and Applications in Homotopy Theory. Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological algebra. Whitehead to meet the needs of homotopy theory.
Other editions – View all Algebraic topology C. Foundations of Combinatorial Topology. The fundamental group of a finite simplicial complex does have a finite presentation. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphismthough usually most classify up to homotopy equivalence. Views Read Edit View history. That is, cohomology is defined as the abstract study of cochainscocyclesand coboundaries. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex.
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 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.
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 to algebraic topology.
Algebraic topology – C. R. F. Maunder – Google Books
An older name for the subject was combinatorial topologyimplying an emphasis on how a space Topolog was constructed from simpler ones  the modern standard tool for such construction is the CW complex. 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.