Knots and Primes
Subtitle: An Introduction to Arithmetic Topology
By: by Masanori Morishita
Contributors: SpringerLink (Online service)
Series: Universitext
Publisher: Springer-Verlag London Limited
Published: 2012
Place of publication: London
Language: eng
Format: [electronic resource] :
Number of pages: 191
ISBN-13: 9781447121572; 9781447121589
Subjects: Mathematics; Mathematics, general; Number theory; Topology
Description: This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory.  Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied  with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.