Work

A note on surfaces in $\mathbb{CP}^2$ and $\mathbb{CP}^2\# \mathbb{CP}^2$

Year: 2022

Type: preprint

Abstract: In this brief note, we investigate the $\mathbb{CP}^2$-genus of knots, i.e. the least genus of a smooth, compact, orientable surface in $\mathbb{CP}^2\setminus \mathring{B^4}$ bounded by a knot in $S^3$. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the $\mathbb{CP}^2$-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in $\mathbb{CP}^2\# \mathbb{CP}^2$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2210.12486

Authors: Marengon, Marco, Miller, Allison N., Ray, Arunima, Stipsicz, András I.

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4307311015

Cites:

Cited by: 1

Related to: 10