An Introduction to Manifolds van Loring W. Tu is an English-language textbook that offers a compact and clear introduction to the mathematical theory of manifolds. The book is suitable for readers who want to delve into this subject and provides a solid foundation for further studies in algebra, topology, and analysis.
The text emphasizes quickly mastering essential concepts in differential geometry and topology. Among other things, the reader learns to compute the de Rham cohomology of simple spaces, a fundamental topological invariant of manifolds. Essential background knowledge such as point-set topology is explained in an appendix, alongside additional information from analytic and linear algebra.
This work is extremely well suited as a course book for advanced undergraduate and master’s students in mathematics. With its clear overview and didactic approach, it prepares the reader for further in-depth study in modern geometry and related fields.
In terms of subject matter, the book fits within the themes of Topology, Calculus and Mathematical Analysis and MATHEMATICS / Topology.
Series: Universitext