Examples of planar tight contact structures with support norm one
Tolga Etg\"u, Yanki Lekili
TL;DR
This paper constructs an infinite family of tight contact structures demonstrating that supporting open books can fail to simultaneously minimize genus and maximize Euler characteristic, addressing a question in contact topology.
Contribution
It provides explicit examples of tight contact structures with supporting open books that do not optimize both genus and Euler characteristic, answering a previously open question.
Findings
Infinite family of tight contact structures constructed
Supporting open books do not always minimize genus
Supporting open books do not always maximize Euler characteristic
Abstract
We exhibit an infinite family of tight contact structures with the property that none of the supporting open books minimizes the genus and maximizes the Euler characteristic of the page simultaneously, answering a question of Baldwin and Etnyre in arXiv:0910.5021 .
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