Menasco co-authors new book, Braid Foliations in Low-Dimensional Topology

William W. Menasco

William W. Menasco

Published October 31, 2017

The American Mathematical Society recently published Braid Foliations in Low-Dimensional Topology, co-authored by UB Mathematics Professor William W. Menasco, and Western Illinois University Professor Douglas J. LaFountain. This book is 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. Professor Menasco is currently serving UB Math as Director of Graduate Studies.

Visual flavor of arguments supported by over 200 figures

With style and content accessible to beginning students interested in geometric topology, each chapter centers around a key theorem or theorems. The particular braid foliation techniques needed to prove these theorems are introduced in parallel, so that the reader has an immediate “take-home” for the techniques involved.

The reader will learn that braid foliations provide a flexible toolbox capable of proving classical results such as Markov's theorem for closed braids and the transverse Markov theorem for transverse links, as well as recent results such as the generalized Jones conjecture for closed braids and the Legendrian grid number conjecture for Legendrian links. Connections are also made between the Dehornoy ordering of the braid groups and braid foliations on surfaces.

All of this is accomplished with techniques for which only mild prerequisites are required, such as an introductory knowledge of knot theory and differential geometry. The visual flavor of the arguments contained in the book is supported by over 200 figures.

Readership includes graduate students and researchers interested in geometry and topology.

The American Mathematical Society has maintained an active publishing program for over 100 years and has established a reputation as one of the top publishers of advanced mathematics.

The AMS Book Program began with our Colloquium series, which has its roots in the famous 1894 lectures of Felix Klein. It has since grown into one of the most respected collections of mathematical literature in the world. We publish nearly 100 new titles each year, including groundbreaking monographs, graduate and undergraduate textbooks, conference proceedings, translations, and works of popular mathematics.