## Algebraic & Geometric Topology

### Compact Stein surfaces as branched covers with same branch sets

Takahiro Oba

#### Abstract

For each integer $N ≥ 2$, we construct a braided surface $S ( N )$ in $D 4$ and simple branched covers of $D 4$ branched along $S ( N )$ such that the covers have the same degrees and are mutually diffeomorphic, but Stein structures associated to the covers are mutually not homotopic. As a corollary, for each integer $N ≥ 2$, we also construct a transverse link $L ( N )$ in the standard contact $3$–sphere and simple branched covers of $S 3$ branched along $L ( N )$ such that the covers have the same degrees and are mutually diffeomorphic, but contact manifolds associated to the covers are mutually not contactomorphic.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 3 (2018), 1733-1751.

Dates
Revised: 20 July 2017
Accepted: 19 September 2017
First available in Project Euclid: 26 April 2018

https://projecteuclid.org/euclid.agt/1524708104

Digital Object Identifier
doi:10.2140/agt.2018.18.1733

Mathematical Reviews number (MathSciNet)
MR3784017

Zentralblatt MATH identifier
06866411

#### Citation

Oba, Takahiro. Compact Stein surfaces as branched covers with same branch sets. Algebr. Geom. Topol. 18 (2018), no. 3, 1733--1751. doi:10.2140/agt.2018.18.1733. https://projecteuclid.org/euclid.agt/1524708104

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