Manifolds, Vector Fields, and Differential Forms

Gal Gross is a Ph.D. student in mathematics at the University of Toronto, working in combinatorics and algebra with a special interest in additive combinatorics. Gross' other mathematical interests include differential geometry, set theory and foundational questions. Eckhard Meinrenken is a professor of mathematics at the University of Toronto, working in the fields of differential geometry and mathematical physics. His contributions include a proof of the Guillemin-Sternberg conjecture in symplectic geometry and the development, with Alekseev and Malkin, of the theory of group-valued momentum maps. In 2002 he was an invited speaker at the ICM in Beijing, and in 2008 he was elected Fellow of the Royal Society of Canada. Meinrenken's book Clifford Algebras and Lie Theory was published (c) 2013 in Springer's Ergebnisse series

• 1. Introduction.- 2. Manifolds.- 3. Smooth maps.- 4. Submanifolds.- 5. Tangent spaces.- 6. Vector fields.- 7. Differential forms.- 8. Integration.- 9. Vector bundles.- Notions from set theory.- Notions from algebra.- Topological properties of manifolds.- Hints and answers to in-text questions.- References.- List of Symbols.- Index.

“This book is intended to be a modern introduction to the basics of differential geometry, accessible to undergraduate and master students. From my point of view, this goal is achieved, the book being very well structured and supported by illustrative examples and problems. … this book will be of great interest for undergraduate students, master students, and also helpful for instructors.” (Gabriel Eduard Vilc, zbMATH 1522.53001, 2023)