Compact Stein surfaces as branched covers with same branch sets

Oba, Takahiro

doi:10.2140/agt.2018.18.1733

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Compact Stein surfaces as branched covers with same branch sets

Takahiro Oba

Algebraic & Geometric Topology 18 (2018) 1733–1751

DOI: 10.2140/agt.2018.18.1733

Abstract

For each integer $N \geq 2$ , 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 $N \geq 2$ , 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.

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

Volume 18, issue 3 (2018)