The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide

A detailed exposition of the theory with an emphasis on its combinatorial aspects.

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, r

This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as k

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to thi