Symplectically replacing plumbings with Euler characteristic 2 4-manifolds

Jonathan Simone

Published 2016-08-17Version 1

A 2-replaceable linear plumbing is defined to be a linear plumbing whose lens space boundary, equipped with the canonical contact structure inherited from the standard contact structure on $S^3$, has a minimal strong symplectic filling of Euler characteristic 2. A 2-replaceable plumbing tree is defined in an analogous way. In this paper, we classify all 2-replaceable linear plumbings, build some families of 2-replaceable plumbing trees, and use one such tree to construct a symplectic exotic $\mathbb{C}P^2#6\bar{\mathbb{C}P}^2$.