On overtwisted, right-veering open books
Paolo Lisca
TL;DR
This paper constructs infinitely many examples of overtwisted, right-veering, non-destabilizable open books on lens spaces, challenging a previous conjecture and expanding understanding of contact structures.
Contribution
It provides the first infinite family of counterexamples to the Honda-Kazez-Matic conjecture using four-holed sphere pages.
Findings
Existence of infinitely many overtwisted, right-veering, non-destabilizable open books
Counterexamples are on lens spaces with four-holed sphere pages
Challenges previous conjectures in contact topology
Abstract
We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our open books is a four-holed sphere and the underlying 3-manifolds are lens spaces.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics