Topology of Numbers
đź“ś Abstract
This book presents the basic concepts and results in algebraic topology from the point of view of the theory of numbers. It includes an introduction to the subject, the classical theory of quadratic forms over the integers, as well as lattices, extensively studied in the last few decades.
✨ Summary
“Topology of Numbers” by Allen Hatcher is a comprehensive text that discusses the intersection of algebraic topology and number theory. Published in March 2004, the book covers foundational topics such as quadratic forms, algebraic integers, lattices, and their connections to homology and hyperbolic geometry. While the text itself does not explicitly list its influence on subsequent research or industry applications, Hatcher’s work is known for its rigorous approach and ability to make complex topics accessible to mathematicians. Recent studies in mathematical structures and hyperbolic geometry often cite this reference due to its foundational explanations and connections between topological and numerical theories. Although there are no direct links to papers citing “Topology of Numbers” in significant applications, the book is frequently used as a supplementary text in upper-level mathematics courses and has contributed to enhancing the understanding of geometric aspects in number theory. For further information on its influence, potential readers may explore university course syllabi and textbooks that incorporate its methodologies and concepts.