Why is a rational blowdown surgery interesting in 4-manifolds?

2024/02/14 水 16:45 - 17:45
Jongil Park
Seoul National University

概要:A rational blowdown surgery initially introduced by R. Fin-tushel and R. Stern and later generalized by J. Park is one of the simple but powerful techniques in study of 4-manifolds topology. Note that a rational blowdown surgery replaces a certain linear chain of embedded 2-spheres by a rational homology 4-ball. In par-ticular, a rational homology ball is a key ingredient in the con-struction of exotic smooth, symplectic 4-manifolds with small Eu-ler characteristic and complex surfaces of general type with pg = 0.
It also plays an important role in Q-Gorenstein smoothings and symplectic filings of the link of normal surface singularities.
In this talk, I review what we have obtained in study of 4-manifolds using a rational blowdown surgery in various levels. And then, I’d like to discuss some open problems in related topics.