Introduction to Geometry and Topology

Werner Ballmann is Professor of Differential Geometry at the University of Bonn and Director at the Max Planck Institute for Mathematics in Bonn.

• I. First Steps in the Topology.- II. Manifolds.- III. Differential Forms and Cohomology.- IV. Geometry of Submanifolds.- A. Alternating Multilinear Forms.- B. Cochain Complexes.- Bibliography.- Index.

“This book is an excellent companion to everyone involved in courses on Differential Topology and/or Differential Geometry. Quite efficiently it gets to several deep results avoiding diversions, still giving a sense of pace friendly to the reader. Otherwise it takes matters till the accesible point and proposes literature for further progress. Strongly recommendable.” (Jesus M. Ruiz, European Mathematical Society, euro-math-soc.eu, February, 2019)“Mathematical exposition has a curatorial aspect. … Along the path to the Stokes theorem, readers meet some undisguised algebraic topology and beyond it get a solid introduction to differential geometry, including the Riemann curvature tensor. Manywill wish they had used this book as students. Summing Up: Recommended. Lower-division undergraduates through faculty and professionals.” (D. V. Feldman, Choice, Vol. 56 (6), February, 2019)