2020/10/06 by Gabriel Islambouli, Islambouli, Gabriel, Patrick Naylor +1
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2010.03057
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.