A note on surfaces in ℂℙ² and ℂℙ²#ℂℙ²

Marengon, Marco and Miller, Allison and Ray, Arunima and Stipsicz, András (2024) A note on surfaces in ℂℙ² and ℂℙ²#ℂℙ². PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY SERIES B, 11 (18). pp. 187-199. ISSN 2330-1511

Preview

Text S2330-1511-2024-00218-X.pdf - Published Version Available under License Creative Commons Attribution. Download (233kB) | Preview

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 .

Actions (login required)

Edit Item