Bøger af Mahima Ranjan Adhikari

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.

This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.

Topics covered in this volume include homotopy theory, homology and cohomology theories, homotopy theory of fiber bundles, Euler characteristic, and the Betti number.

In addition to the group, ring and module theory usually found in a standard modern algebra text, this book discusses group theory, semigroups, groups, topological groups and Lie groups, factorization theory, Noetherian and Artinian rings and more.