Markov's Theorem and 100 Years of the Uniqueness Conjecture A Mathematical Journey from Irrational Numbers to Perfect Matchings /

• Main Author: Aigner, Martin (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Springer, 2013.
• Subjects: Mathematics.; Group theory.; Number theory.; Combinatorics.; Number Theory.; Group Theory and Generalizations.

This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme...

Table of Contents:

• Approximation of Irrational Numbers
• Markov's Theorem and the Uniqueness Conjecture
• The Markov Tree
• The Cohn Tree
• The Modular Group SL(2,Z)
• The Free Group F2
• Christoffel Words
• Sturmian Words
• Proof of Markov's Theorem
• The Uniqueness Conjecture.  .