%0 Journal Article
%T The nonorientable four-genus of knots
%A Patrick M. Gilmer
%A Charles Livingston
%J Mathematics
%D 2010
%I arXiv
%R 10.1112/jlms/jdr024
%X We develop obstructions to a knot K in the 3-sphere bounding a smooth punctured Klein bottle in the 4-ball. The simplest of these is based on the linking form of the 2-fold branched cover of the 3-sphere branched over K. Stronger obstructions are based on the Ozsvath-Szabo correction term in Heegaard-Floer homology, along with the G-signature theorem and the Guillou-Marin generalization of Rokhlin's theorem. We also apply Casson-Gordon theory to show that for every n greater than one there exists a knot that does not bound a topologically embedded nonorientable ribbon surface F in the 4-ball with first Betti number less than n.
%U http://arxiv.org/abs/1005.5473v3