Chapter 4 - Knot Spinning

Abstract

There are many important ways to construct higher dimensional knots. This chapter focuses on algebraic knots, also examining the links of singularities of complex algebraic varieties. The chapter explains spinning constructions for higher-dimensional knots. These methods for creating new knots from knots of lower dimension can be described geometrically, and so spun knots often can be visualized directly (or at least schematically). The chapter then describes the basics of higher-dimensional knot theory and then turns to specific constructions, including simple spinning, superspinning, twist spinning, frame spinning, rolling, and deform spinning. It then discusses some new hybrid constructions, such as frame twist spinning, frame deform spinning, and frame rolling. Examples of important historical applications and results are illustrated.