Basic Algebraic Topology and its Applications

Mahima Ranjan Adhikari (Autor)

Buch | Softcover

615 Seiten

2018 | Softcover reprint of the original 1st ed. 2016
Springer, India, Private Ltd (Verlag)
978-81-322-3855-3 (ISBN)

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This book provides an accessible introduction to algebraic topology, a ﬁeld 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 oﬀers 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.

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 ﬁve 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.

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.

Erscheinungsdatum	02.09.2018
Zusatzinfo	176 Illustrations, black and white; XXIX, 615 p. 176 illus.
Verlagsort	New Delhi
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	cohomology operations • Eilenberg-Steenrod axioms • Generalized cohomology • Homology and cohomology group • Homotopy and cohomotopy group • Hopf invariant and Knot group • Spectrum of spaces • vector bundle
ISBN-10	81-322-3855-9 / 8132238559
ISBN-13	978-81-322-3855-3 / 9788132238553
Zustand	Neuware