A Ludic Journey into Geometric Topology

This book draws on elements from everyday life, architecture, and the arts to provide the reader with elementary notions of geometric topology. Pac Man, subway maps, and architectural blueprints are the starting point for exploring how knowledge about geometry and, more specifically, topology has been consolidated over time, offering a learning journey that is both dense and enjoyable. The text begins with a discussion of mathematical models, moving on to Platonic and Keplerian theories that explain the Cosmos. Geometry from Felix Klein's point of view is then presented, paving the way to an introduction to topology. The final chapters present the concepts of closed, orientable, and non-orientable surfaces, as well as hypersurface models. Adopting a style that is both rigorous and accessible, this book will appeal to a broad audience, from curious students and researchers in various areas of knowledge to everyone who feels instigated by the power of mathematics in representing our world - and beyond.

Explores real-world elements to introduce non-specialists to geometric topology Offers a rich learning journey that is both dense and enjoyable Engages everyone who feels intrigued by the power of mathematics in explaining the world

Auteur

Ton Marar is an Associate Professor at the Institute of Mathematics and Computer Sciences, University of São Paulo at São Carlos, Brazil. He holds a Master's degree (1983) in Mathematics (Geometry) from the same university, and a PhD (1989) from the University of Warwick, United Kingdom. His research fields include singularity theory and geometric topology or, more specifically, geometry and classification of singular surfaces and geometric aspects of singularities of maps.

Résumé

"Each section ends with a list of suggested reading ... . the text should be approachable to anyone who is at least moderately interested in mathematics. ... I think it would make a great source of entertaining supplemental reading for an undergraduate course related to geometry or topology." (Timothy Clark, MAA Reviews, March 29, 2024)

"This book is an excellent introduction to geometry and topology, for people who do not know much about these subjects. ... This book constitutes a very interesting reading for any advanced high-school pupil and for non-mathematicians. It should be also useful for university undergraduates. Geometers and topologists will also find it pleasant to skim, because of the historical remarks, the questions and relations that the author establishes between geometry and topology and the things of everyday life." (Athanase Papadopoulos, zbMATH 07555479, 2023)

Contenu
Preface.- Mathematical Models.- The Big Bang Theory of Ancient Greece.- Geometry: From disorder to order.- Topology.- Fourth dimension.- Non-orientable surfaces.- Hypersurfaces.