Journal of Symplectic Geometry

Volume 19 (2021)

Number 5

Generalized chain surgeries and applications

Pages: 1047 – 1069



Anar Akhmedov (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Çağrı Karakurt (Department of Mathematics, Boğaziçi University, Bebek, İstanbul, Turkey)

Sümeyra Sakallı (Department of Mathematical Sciences, University of Arkansas, Fayetteville, Ark., U.S.A.)


We describe the Stein handlebody diagrams of Milnor fibers of Brieskorn singularities $x^p + y^q + z^r = 0$. We also study the natural symplectic operation by exchanging two Stein fillings of the canonical contact structure on the links in the case $p = q = r$, where one of the fillings comes from the minimal resolution and the other is the Milnor fiber. We give two different interpretations of this operation, one as a symplectic sum and the other as a monodromy substitution in a Lefschetz fibration.

Received 18 June 2020

Accepted 24 January 2021

Published 27 May 2022