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This third of the three-volume book is targeted as a basic course in algebraic topology and topology for fiber bundles for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, and algebra. Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number. It also includes certain classic problems such as the Jordan curve theorem along with the discussions on higher homotopy groups and establishes links between homotopy and homology theories, axiomatic approach to homology and cohomology as inaugurated by Eilenberg and Steenrod. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power and active learning of the subject, all the while covering a wide range of theory and applications in a balanced unified way.
Prerequisite Concepts of Algebra, Topology, Manifold and Category Theory
Homotopy Theory: Fundamental Group and Higher Homotopy Groups
Homology and Cohomology Theories: An Axiomatic Approach with Consequences
Topology of Fiber Bundles: General Theory of Bundles
Topology of Fiber Bundles: Homotopy Theory of Bundles
Geometric Topology and Further Applications of Algebraic Topology
Brief History of Algebraic Topology: Motivation of the Subject and Historical Development