Description
Book SynopsisOffers a self-contained introduction to braid foliation techniques, which is a theory developed to study knots, links and surfaces in general 3-manifolds and more specifically in contact 3-manifolds. With style and content accessible to beginning students interested in geometric topology, each chapter centres around a key theorem or theorems.
Trade ReviewThis research monograph is a highly readable and pleasant introduction to the toolkits that the authors call braid foliation techniques, a small but relatively underdeveloped corner of low-dimensional topology and geometry. It is written at a level that will be accessible to graduate students and researchers and is carefully structured and filled with useful examples." — J.S. Birman,
Mathematical Reviews"The AMS once more presents the mathematical community with a strong text geared to getting graduate students and other relative beginners into the game. The present book is thorough and well-structured, leads the reader pretty deeply into the indicated parts of knot and link-theory and low-dimensional topology and does so effectively and (as far as I can tell) rather painlessly...All in all, the book looks like a hit." — Michael Berg,
MAA ReviewsTable of Contents
- Links and closed braids
- Braid foliations and Markov's theorem
- Exchange moves and Jones' conjecture
- Transverse links and Bennequin's inequality
- The transverse Markov theorem and simplicity
- Botany of braids and transverse knots
- Flypes and transverse nonsimplicity
- Arc presentations of links and braid foliations
- Braid foliations and Legendrian links
- Braid foliations and braid groups
- Open book foliations
- Braid foliations and convex surface theory
- Bibliography
- Index.
