A Note On Surfaces in ℂℙ² And ℂℙ²#ℂℙ²

Authors

M. Marengon
Allison N. Miller, Swarthmore CollegeFollow
A. Ray
A. I. Stipsicz

Document Type

Article

Publication Date

6-24-2024

Published In

Proceedings Of The American Mathematical Society Series B

Abstract

In this brief note, we investigate the ℂℙ²-genus of knots, i.e., the least genus of a smooth, compact, orientable surface in ℂℙ² \ \mathringB⁴ bounded by a knot in 𝑆³. We show that this quantity is unbounded, unlike its topological counterpart. We also investigate the ℂℙ²-genus of torus knots. We apply these results to improve the minimal genus bound for some homology classes in ℂℙ²#ℂℙ².

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

Comments

This work is freely available under a Creative Commons license.

Recommended Citation

M. Marengon, Allison N. Miller, A. Ray, and A. I. Stipsicz. (2024). "A Note On Surfaces in ℂℙ² And ℂℙ²#ℂℙ²". Proceedings Of The American Mathematical Society Series B. Volume 11, 187-199. DOI: 10.1090/bproc/218
https://works.swarthmore.edu/fac-math-stat/315