Eine spielerische Reise in die geometrische Topologie

This book draws on elements from everyday life, architecture, and art to convey fundamental concepts of geometric topology to the reader. Pac-Man, subway maps, and architectural designs serve as starting points for exploring how knowledge of geometry, and particularly topology, has solidified over time, offering an entertaining and exciting learning journey. The text begins with a discussion of mathematical models and progresses to theories from Plato and Kepler that explain the cosmos. It then presents geometry from Felix Klein's perspective, paving the way for an introduction to topology. In the final chapters, the concepts of closed, orientable, and non-orientable surfaces, as well as models of hypersurfaces, are introduced. This book, which is both mathematically rigorous and accessible, will appeal to a wide audience, from curious students and researchers in various fields of knowledge to anyone intrigued by the power of mathematics in representing our world—and beyond. The translation was carried out with the help of artificial intelligence, followed by a subsequent human review, particularly regarding the content.