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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K-theory Lie algebroid Lie groupoid Important publications in algebraic topology Serre spectral sequence Sheaf Topological quantum field theory.
Cohomology Operations and Applications in Homotopy Theory. Homotopy and Simplicial Complexes. 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. Cohomology can be viewed as a method of assigning algebraic invariants mmaunder a topological space that has a more refined algebraic structure than does homology.
The author has given much attention to detail, yet ensures that the reader knows where he is going. 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.
This page was last edited on 11 Octoberat Selected pages Title Page. 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. Courier Corporation- Mathematics – pages. Maunder Courier Corporation- Mathematics – pages 2 Reviews https: That is, cohomology is defined as the abstract study of cochainscocyclesand coboundaries.
Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The author has given much attention to detail, yet ensures that the reader knows where he is going.
Finitely generated abelian groups are completely classified and are particularly easy to work with. Cohomology and Duality Theorems. They defined homology and cohomology as functors equipped with natural transformations subject to certain axioms e.
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. 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.
Other editions – View all Algebraic topology C. 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.
Views Read Edit View tppology. From Wikipedia, the free encyclopedia. Knot theory is the study of mathematical knots. 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.
For the topology of pointwise convergence, see Algebraic topology object.
Algebraic topology – C. R. F. Maunder – Google Books
Homology and cohomology groups, on the other hand, are abelian and in algdbraic important cases finitely generated. Retrieved from ” https: Whitehead to meet the needs of homotopy theory.
In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation algebraaic homeomorphism or more general homotopy of spaces. In less abstract language, cochains in the fundamental sense should assign ‘quantities’ to the chains of homology theory. Introduction to Knot Theory. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician’s knot differs in algerbaic the ends are joined together so that it cannot be undone.
No eBook available Amazon. My library Help Advanced Book Search. The purely combinatorial counterpart to a simplicial complex tooology an abstract simplicial complex. Algebraic K-theory Exact sequence Glossary of algebraic topology Grothendieck topology Higher category theory Higher-dimensional algebra Homological algebra.
Simplicial complex and CW complex. Two major ways in which this can be done are through fundamental groupsor akgebraic generally homotopy theoryand through homology and cohomology groups. In other projects Wikimedia Commons Wikiquote. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphismthough usually most classify up to homotopy equivalence. In general, all constructions of algebraic topology are functorial ; the notions of categoryfunctor and natural transformation originated here.
This class of spaces is broader and has some better algevraic properties than simplicial complexesbut still retains a combinatorial nature that allows for computation often with a much smaller complex. 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.
This allows one to recast statements about topological spaces into statements about groups, which have a great deal of manageable structure, algebraaic making these statement easier to prove. Algebraic topology is a branch of mathematics that uses topllogy from abstract algebra to study topological spaces.
Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.