Volume 18, issue 3 (2018)

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Compact Stein surfaces as branched covers with same branch sets

Takahiro Oba

Algebraic & Geometric Topology 18 (2018) 1733–1751
Abstract

For each integer N 2, we construct a braided surface S(N) in D4 and simple branched covers of D4 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 S3 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.

Keywords
compact Stein surfaces, branched coverings, Lefschetz fibrations, contact manifolds
Mathematical Subject Classification 2010
Primary: 57M12, 57R17
Secondary: 32Q28, 57R65
References
Publication
Received: 18 April 2017
Revised: 20 July 2017
Accepted: 19 September 2017
Published: 3 April 2018
Authors
Takahiro Oba
Department of Mathematics
Tokyo Institute of Technology
Tokyo
Japan