Name Kouichi Yasui Hiroshima University Session Jan 9 14:50~15:20 E11-101 Nuclei and exotic 4-manifolds We introduce a new generalization of Gompf nuclei and give applications. We construct infinitely many exotic smooth structures for a large class of compact 4-manifolds with boundary, regarding topological invariants and boundary 3-manifolds. To detect smooth structures using the adjunction inequality, we introduce a relative genus function. Time permitting, we also construct arbitrary many compact Stein 4-manifolds and infinitely many non-Stein 4-manifolds which are all homeomorphic but mutually non-diffeomorphic. 101-1-9/yasui.pdf