The nonorientable four-genus of knots

Details The nonorientable four-genus of knots The nonorientable four-genus of knots

2010-05-29

arxiv.org/abs/1005.5473v3

Mathematics

Geometric Topology

20 pages; expository changes

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The nonorientable four-genus of knots does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The nonorientable four-genus of knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The nonorientable four-genus of knots will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-86451