ABSTRACT

Knots can be found and used in a variety of situations in the 3D world, such as in vines, in the DNA, polymer chains, electrical wires, in mountaineering, seamanship and when ropes or other flexible objects are involved for exerting forces and holding objects in place. Research on knots as topological entities has contributed with a number of findings, not only of interest to pure mathematics, but also to statistical mechanics, quantum physics, genetics, and chemistry. Yet, the cognitive (or algorithmic) aspects involved in the act of tying a knot are a largely uncharted territory. This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational (including robotics) standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.

摘要

可以在3D世界中的各种情况下找到并使用结，例如在藤蔓，DNA，聚合物链，电线，登山，航海以及涉及绳索或其他柔性物体以施加力和固定物体的情况下到位。对作为拓扑实体的结的研究已经产生了许多发现，不仅对纯数学感兴趣，而且对统计力学，量子物理学，遗传学和化学也很有意义。然而，打结动作所涉及的认知（或算法）方面基本上是未知的领域。本文从拓扑，物理，认知和计算（包括机器人学）的角度对与打结研究相关的文献进行了综述，