Mathematical Research Letters

Volume 27 (2020)

Number 1

Surfaces in the $4$-disk with the same boundary and fundamental group

Pages: 265 – 279



Takahiro Oba (Department of Mathematics, Tokyo Institute of Technology, Meguroku, Tokyo, Japan; and Research Institute of Mathematical Sciences, Kyoto University, Kyoto, Japan)


We construct a family of pairs of non-isotopic symplectic surfaces in the standard symplectic $4$‑disk ($D^4, \omega_{st})$ such that they are bounded by the same transverse knot in the standard contact $3$‑sphere and the fundamental groups of their complements are isomorphic.

This work was supported by JSPS KAKENHI Grant Number 15J05214.

Received 1 August 2018

Accepted 12 February 2019

Published 8 April 2020