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A Ludic Journey into Geometric Topology

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  • © 2022


  • 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

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Table of contents (7 chapters)


About this book

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. 


“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)

Authors and Affiliations

  • ICMC, University of São Paulo at São Carlos, São Carlos, Brazil

    Ton Marar

About the author

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.

Bibliographic Information

  • Book Title: A Ludic Journey into Geometric Topology

  • Authors: Ton Marar

  • DOI:

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-07441-7Published: 02 September 2022

  • Softcover ISBN: 978-3-031-07444-8Published: 03 September 2023

  • eBook ISBN: 978-3-031-07442-4Published: 01 September 2022

  • Edition Number: 1

  • Number of Pages: XIV, 115

  • Number of Illustrations: 45 b/w illustrations, 123 illustrations in colour

  • Topics: Geometry, Topology, Mathematics, general

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