Abstract
In this brief note, we investigate the C P 2 \mathbb {CP}^2 -genus of knots, i.e., the least genus of a smooth, compact, orientable surface in C P 2 ∖ B 4 ˚ \mathbb {CP}^2\smallsetminus \mathring {B^4} bounded by a knot in S 3 S^3 . We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the C P 2 \mathbb {CP}^2 -genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in C P 2 # C P 2 \mathbb {CP}^2\# \mathbb {CP} ^2 .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the American Mathematical Society, Series B
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
