Unbraided wiring diagrams for Stein fillings of lens spaces
Mohan Bhupal, Burak Ozbagci

TL;DR
This paper provides an algorithm to draw unbraided wiring diagrams for Stein fillings of lens spaces, linking Lefschetz fibrations, symplectic disk arrangements, and cyclic quotient singularities, with applications to classifying Stein fillings.
Contribution
It introduces a new algorithm for unbraided wiring diagrams that represent Stein fillings, connecting Lefschetz fibrations, symplectic geometry, and singularity theory.
Findings
Wiring diagrams can be extended to symplectic disk arrangements in ^2.
The arrangement relates to the cyclic quotient singularity's plane curve germ.
A bijection between Stein fillings and Milnor fibers is explicitly constructed.
Abstract
In a previous work, we constructed a planar Lefschetz fibration on each Stein filling of any lens space equipped with its canonical contact structure. Here we describe an algorithm to draw an unbraided wiring diagram whose associated planar Lefschetz fibration obtained by the method of Plamenevskaya and Starkston, where the lens space with its canonical contact structure is viewed as the contact link of a cyclic quotient singularity, is equivalent to the Lefschetz fibration we constructed on each Stein filling of the lens space at hand. Coupled with the work of Plamenevskaya and Starkston, we obtain the following result as a corollary: The wiring diagram we describe can be extended to an arrangement of symplectic graphical disks in with marked points, including all the intersection points of these disks, so that by removing the proper transforms of these disks from the…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques
