Abstract. We investigate the bi-orderability of two-bridge knot groups and the groups of knots with or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst all knots with or fewer crossings (of which there are ), previous theorems were only able to determine bi-orderability of of the corresponding knot groups. With our methods we are able to deal with more.

We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations E(n)p,q all admit genus 3 multisections, and draw explicit diagrams for these manifolds.

No abstract

We introduce multisections of smooth, closed 4-manifolds, which generalize trisections to decompositions with more than three pieces. This decomposition describes an arbitrary smooth, closed 4-manifold as a sequence of cut systems on a surface. We show how to carry out many smooth cut and paste operations in terms of these cut systems. In particular, we show how to implement a cork twist, whereby we show that an arbitrary exotic pair of smooth 4-manifolds admit 4-sections differing only by one cut system. By carrying out fiber sums and log transforms, we also show that the elliptic fibrations E ( n ) p , q E(n)_{p,q} all admit genus 3 3 multisections, and draw explicit diagrams for these manifolds.

No abstract