Homology And Cohomology

A Primer For Undergraduates Through Applications

Luca Vitagliano (Universita Di Salerno, Italy)

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English

World Scientific Publishing Co Pte Ltd
15 May 2025

Algebraic geometry; Algebraic topology

Summary
Details

The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergraduate Mathematics students, as well as graduate and postgraduate students in other fields, particularly Theoretical Physics, who require a highly compact overview of this vast theory. The book also explores how (co)homology theory naturally arises in seemingly unrelated areas of Mathematics.

The theory is presented from scratch, requiring no prerequisites other than basic linear algebra, point-set topology, and calculus. The presentation is simple, concise, yet rigorous, making it accessible to undergraduate Mathematics and likely Physics students from the third year onward. The book emphasizes the theory's numerous applications across Algebra and Geometry, rather than focusing solely on the theoretical aspects. The pedagogical approach of this book, complemented by examples and exercises, sets it apart from standard textbooks in Homological Algebra and Algebraic Topology. The end-of-chapter problems offer insight into more advanced material and serve as a tool for testing comprehension of the theory.

After having gone through these lecture notes, the reader will be ready to tackle more specialized and advanced subjects such as Homological Algebra, Homotopy Theory, and Algebraic Topology.

By: Luca Vitagliano (Universita Di Salerno Italy)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789819807109
ISBN 10: 9819807107
Pages: 272
Publication Date: 15 May 2025
Audience: College/higher education , Professional and scholarly , A / AS level , Undergraduate
Format: Paperback
Publisher's Status: Active