Bridge trisections in rational surfaces

We study smooth isotopy classes of complex curves in complex surfaces from the perspective of the theory of bridge trisections, with a special focus on curves in $\mathbb{CP}^2$ and $\mathbb{CP}^1\times\mathbb{CP}^1$. We are especially interested in bridge trisections and trisections that are as simple as possible, which we call "efficient". We show that any curve in $\mathbb{CP}^2$ or $\mathbb{CP}^1\times\mathbb{CP}^1$ admits an efficient bridge trisection. Because bridge trisections and trisections are nicely related via branched covering operations, we are able to give many examples of complex surfaces that admit efficient trisections. Among these are hypersurfaces in $\mathbb{CP}^3$, the elliptic surfaces $E(n)$, the Horikawa surfaces $H(n)$, and complete intersections of hypersurfaces in $\mathbb{CP}^N$. As a corollary, we observe that, in many cases, manifolds that are homeomorphic but not diffeomorphic have the same trisection genus, which is consistent with the conjecture that trisection genus is additive under connected sum. We give many trisection diagrams to illustrate our examples.Comment: 46 pages, 28 color figure

Perth freight link: good idea, wrong port

The Perth Freight Link (PFL) has been announced as a major transport opportunity to solve the heavy goods truck problems in Perth. By taking trucks via a toll road around an extended Roe Highway, through Stock Road and Leach Highway to the Fremantle Inner Harbour it has been proposed to alleviate the current congestion and match the expected increase in truck traffic over the coming years. This paper takes a contrary view by analyses and suggests that the PFL is very poor planning; it is likely to harm the city of Fremantle and damage the operations of the port. The findings demonstrate the real need is to create good road and rail connections to a new container port in the Fremantle Outer Harbour

The Process of Learning

Biggs, J. B. and Moore, P.J. (1993) The Process of Learning (3rd ed.) Sydney : Prentice Hall. 582 p