Séminaire de géométrie algébrique

Marco Marengon (virtuel): Relative genus bounds in indefinite 4-manifolds

001 (batiment I)


batiment I

Département de mathématiques Bâtiment I Faculté des Sciences 2 Boulevard Lavoisier F-49045 Angers cedex 01 France

Given a closed 4-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X-int(B^4), with boundary a given knot K in the 3-sphere. We give several methods to bound the genus of such surfaces in a fixed homology class. Our techniques include adjunction inequalities from Heegaard Floer homology and the Bauer-Furuta invariants, and the 10/8 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disc) in a 4-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. This is joint work with Ciprian Manolescu and Lisa Piccirillo.