After reviewing methods for constructing exotic smooth structures on closed four-manifolds, we examine the ‘genus-function’ on the second homology, and ask/answer some questions related to this function. We extend the notion to manifolds with boundary, where the surfaces are bounded by knots or links in the boundary. We examine the relevance of these notions for the Smooth Four-dimensional Poincare Conjecture.
By Mélanie Bertelson
By Jean-Paul Mohsen
By Mohammed Abouzaid
By Ailsa Keating
By Daniel Alvarez-Gavela
By Kyler Siegel
By András Stipsicz
By Ko Honda
By Yu Pan
By Oleg Lazarev
By Paul Biran
By Ana Rechtman
By Albert Schwarz
By Albert Schwarz
By Juan Camilo Arosemena Serrato
By Pieter Spaas
By Amine Marrakchi
By Francesca Arici
