Homotopy theory

Author: Jiang Boju
Publisher:
Publish Date: 2006-02-01
Features: This book serves as a foundational course textbook for graduate students in mathematics departments of comprehensive universities and normal universities. It is divided into five chapters, systematically covering the fundamental theories and methods of homology theory. The main thread of the book is the theoretical framework of singular homology and the computational methods of cellular homology, with simplicial homology treated as a special case of cellular homology. The first three chapters discuss additive structures, largely following traditional approaches. Chapter four explores multiplicative structures, integrating perspectives from both singular and cellular homology. Chapter five presents a novel discussion of manifolds, establishing a symmetric dual decomposition on cellular manifolds, providing a clear geometric visualization for dual theorems. Though this approach is classical, it is unprecedented in the literature. The book emphasizes concepts, methods, conclusions, and applications in its selection, fully reflecting the core content of homology theory. In its content presentation, it highlights geometric backgrounds, offers rich examples, and is illustrated with diagrams. The narrative is concise yet clear, with attention to the connections and coherence between chapters, facilitating both teaching and self-study. Each section is accompanied by a sufficient number of exercises and reflection questions to aid readers in understanding and mastering the material. This book can serve as a textbook or teaching reference for graduate students in mathematics at comprehensive universities and normal universities, as well as for senior undergraduate students. It is also suitable for mathematicians to read.