Hironobu NAOE

Title: Shadow-complexity of corks and exotic pairs of 4-manifolds

Abstract:
The (special) shadow-complexity is an invariant of 3- and 4-manifolds that measures how simple/complicated they are.
We study shadow-complexities of corks which are a crucial notion in the study of exotic smooth structures of 4-manifolds.
In this talk, we show that there are infinitely many mutually non-diffeomorphic corks with arbitrary large special shadow-complexity.
We also discuss Costantino's question on the minimal (special) shadow-complexity of exotic pairs.