Cubical Homotopy Theory

This resourceful book offers a deep dive into homotopy theory, focusing on cubical diagrams, making it suitable for graduate students and researchers.

In Cubical Homotopy Theory, graduate students and researchers are presented with a comprehensive exploration of both classical and contemporary topics in topology. This book stands out for its modern treatment of homotopy theory, particularly through the lens of cubical diagrams. With 300 examples provided, readers will find detailed explanations of fundamental results that are essential for diving into the more intricate areas of research in topology. The structured approach ensures that even those new to the subject can grasp complex concepts with relative ease.

The first part of Cubical Homotopy Theory establishes foundational material on homotopy theory, focusing on key topics such as fibrations, cofibrations, and the Blakers–Massey Theorem. By emphasizing cubical diagrams, the book allows for a unique perspective on homotopy pullbacks and pushouts. The second part serves as an introduction to categories, limits, and colimits, providing readers with an accessible account of homotopy limits and colimits of diagrams of spaces, as well as cosimplicial spaces.

Concluding with applications to innovative areas using cubical diagrams, Cubical Homotopy Theory offers an overview of calculus of functors and delves into recent advancements in knot topology. This book is an essential resource for anyone looking to understand the modern landscape of homotopy theory through practical examples and clear explanations.