Basic Algebraic Topology and its Applications

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Beschreibung

This book provides an accessible introduction to algebraic topology, a ¿eld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book öers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike.

Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Über den Autor

Mahima Ranjan Adhikari, PhD, is a former professor of Pure Mathematics at the University of Calcutta. His main interest lies in algebra and topology. He has published a number of papers in several international journals including the Proceedings of American Mathematical Society and ¿ve textbooks. Eleven students have already been awarded the PhD degree under his supervision. He is a member of the American Mathematical Society and serves on the editorial board of several journals and research monographs. He was the president of the mathematical science section of the 95th Indian Science Congress, 2008.

He has visited several institutions in India, USA, UK, Japan, France, Greece, Sweden, Switzerland, Italy and many other countries on invitation. While visiting E.T.H., Zurich, Switzerland, in 2003, he made an academic interaction with Professor B Eckmann and P J Hilton. He is currently the president of the Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC). He is also the principal investigator of an ongoing project funded by the Government of India.

The present book is written based on author's teaching experience of 50 years. He is the joint author ( with Avishek Adhikari) of another Springer book "Basic Modern Algebra with Applications", 2014.

Zusammenfassung

Discusses the basic concepts of algebraic topology with numerous related illustrations and applications

Approaches the topic nearly "from scratch" and accompanies students through its natural development

Provides examples and step-by-step instructions and explains problem-solving techniques for a better grasp of the topic

Integrates various concepts of algebraic topology, examples, exercises, applications, and historical notes

Reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to pursue further study

Includes supplementary material: [...]

Inhaltsverzeichnis

Prerequisite Concepts and Notations.- Basic Homotopy.- The Fundamental Groups.-Covering Spaces.- Fibre Bundles, Vector Bundles and K-theory.- Geometry of Simplicial Complexes and Fundamental Groups.- Higher Homotopy Groups.- Products in Higher Homotopy Groups.- CW-complexes and Homotopy.- Eilenberg-MacLane Spaces.- Homology and Cohomology Theories.- Eilenberg-Steenrod Axioms for Homology and Cohomology Theories.- Consequences of the Eilenberg-Steenrod Axioms.- Some Applications of Homology Theory.- Spectral Homology and Cohomology Theories.- Obstruction Theory.- More Relations Between Homotopy and Homology Groups.- A Brief Historical Note.

Details

Erscheinungsjahr:	2018
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxix 615 S. 176 s/w Illustr. 615 p. 176 illus.
ISBN-13:	9788132238553
ISBN-10:	8132238559
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Adhikari, Mahima Ranjan
Auflage:	Softcover reprint of the original 1st ed. 2016
Hersteller:	Springer India Springer India Ltd.
Maße:	235 x 155 x 35 mm
Von/Mit:	Mahima Ranjan Adhikari
Erscheinungsdatum:	15.06.2018
Gewicht:	0,966 kg

Artikel-ID: 113999716