Books

This book is a compendium of problems in low-dimensional topology, each presented with background and references. It is aimed at graduate students and more experienced researchers alike, highlighting the problem-driven nature of the field. The problems are intended to stimulate research and point to new directions in an area that has been extremely active and has broadened tremendously over the past 50 years. The problem list is the outcome of a collaborative, community-driven effort that began at a week-long workshop at the American Institute of Mathematics in Fall 2023 and grew substantially through the involvement of chapter editors, workshop participants, problem proposers, scribes, and referees—altogether drawing contributions from several hundred researchers, from early-career mathematicians to senior figures in the field. As in the influential problem lists compiled by R. Kirby in the 1970s and 1990s, the book is organized roughly by dimension: knot theory, surfaces, 3-manifolds, 4-manifolds, and a brief miscellanea chapter. It features close to 400 problems across a wide range of topics, with nearly a thousand subproblems, questions, and conjectures interspersed throughout.

A preliminary version of the book will be made available after the publication, while the official version will be available for purchase from the AMS either in print or electronic format.  Periodic updates will be posted on the book’s home page on the AMS bookstore.

The K3 project was featured in the 2024 Quanta article “A new agenda for low dimensional topology”.

There is a separate effort underway to provide updates for K2, Kirby’s 1997 problem list. Please feel free to reach out to me or Danny Ruberman for any updates you may have.

There has been a long history of rich and subtle connections between low dimensional topology, mapping class groups and geometric group theory. From July 1 to July 5, 2013, the conference “Interactions between low dimensional topology and mapping class groups” held at the Max Planck Institute for Mathematics in Bonn highlighted these diverse connections, and fostered new and unexpected collaborations between researchers in these areas. The proceedings for this conference aims to further draw attention to the beautiful mathematics emerging from diverse interactions between these areas. The articles collected in this volume, in addition to gathering new results, also contain expositions and surveys of the latest developments in various active areas of research at the interface of mapping class groups of surfaces and the topology and geometry of 3– and 4–dimensional manifolds. Many open problems and new directions for research are discussed.

This is a book on traditional draughts game, aka “dama”, a unique version of checkers considered as the closest cousin of chess. Contains anthropological analysis, visual recordings, short stories, and a detailed treatment of tactics and strategies in the game.

Damaya Güzelleme was featured in the 2016 Agenda by the Hrant Dink Foundation. Here is an English excerpt from the agenda: “[Dama’s] history stretches as far back as the Ur, Egyptian, and Ancient Greek civilizations. It is a unique and innovative mind game known for the multiple possibilities of moves and a dynamism which engenders ample opportunity for the effective use of imagination. There are approximately ten simple rules for moves to be organized collectively with pieces which by themselves have limited power. Sacrifices are the main means for gains. Renowned master players from different backgrounds like shoeshine man İbrahim Bey, the rival of Sultan Abdulaziz, became famous more for the refinement of their games than their invincibility.”