Homology And Cohomology: A Primer For Undergraduates Through Applications
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A01=Luca Vitagliano
Algebraic Topology
Author_Luca Vitagliano
Categories and Functors
Category=PBMW
Category=PBPD
Chevalley-Eilenberg Cohomology
Cohomology
de Rham Cohomology
Differential Forms
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Group Homology
Hochschild Homology
Homology
Homotopy
Multilinear Algebra
Simplicial Sets
Singular Homology
Product details
- ISBN 9789819805822
- Publication Date: 09 May 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
