2022/09/26 by Ballinger, William
#57K40 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2209.12851
By taking the complements of embeddings of sphere plumbings in connected sums of ℂ P2, we construct examples of simply connected four-manifolds with lens space boundary and b2 = 1. The resulting boundaries include many lens spaces that cannot come from integer surgery on any knot in S3, so the corresponding four-manifolds cannot be built by attaching a single two-handle to B4. Using similar constructions, we give an example of an embedded sphere in #4 ℂ P2 with self-intersection number 20, and conjecture that this is the maximum possible.