Admissible transverse surgery does not preserve tightness
Abstract
We produce the first examples of closed, tight contact 3-manifolds which become overtwisted after performing admissible transverse surgeries. Along the way, we clarify the relationship between admissible transverse surgery and Legendrian surgery. We use this clarification to study a new invariant of transverse knots - namely, the range of slopes on which admissible transverse surgery preserves tightness - and to provide some new examples of knot types which are not uniformly thick. Our examples also illuminate several interesting new phenomena, including the existence of hyperbolic, universally tight contact 3-manifolds whose Heegaard Floer contact invariants vanish (and which are not weakly fillable); and the existence of open books with arbitrarily high fractional Dehn twist coefficients whose compatible contact structures are not deformations of co-orientable taut foliations.
Cite
@article{arxiv.1203.2993,
title = {Admissible transverse surgery does not preserve tightness},
author = {John A. Baldwin and John B. Etnyre},
journal= {arXiv preprint arXiv:1203.2993},
year = {2012}
}
Comments
26 pages, 2 figures, references and discussion in the introduction and abstract corrected