Algebraic & Geometric Topology

Compact Stein surfaces as branched covers with same branch sets

Takahiro Oba

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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
Received: 18 April 2017
Revised: 20 July 2017
Accepted: 19 September 2017
First available in Project Euclid: 26 April 2018

Permanent link to this document
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

Subjects
Primary: 57M12: Special coverings, e.g. branched 57R17: Symplectic and contact topology
Secondary: 32Q28: Stein manifolds 57R65: Surgery and handlebodies

Keywords
compact Stein surfaces branched coverings Lefschetz fibrations contact manifolds

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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