Tight contact structures with no symplectic fillings

By John B. Etnyre, K. Honda. 2000

113 citations recorded by the source corpus.

Abstract.We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e47f19f0ef67e4faabea216a03ef0ca122e0c45b

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

Weak and strong fillability of higher dimensional contact manifolds (2011, methodology): “Both of these are proper inclusions: in the first case this was shown by Eliashberg [16], and in the second by Etnyre and Honda [20], though today a simple alternative construction is also available using the notion of Giroux torsion.”
Right-veering diffeomorphisms of compact surfaces with boundary (2005, background): “Contact structures which are tight but are not fillable were fi rst discovered by Etnyre-Honda [ EH ] and expanded to infinitely many examples in a series of papers by Lisca-Stipsicz (see [LS1, LS2] for the first couple).”
Four dimensions from two in symplectic topology (2002, background): “There are several notions of fillability of contact manifolds; any one of them suffices in the above theorem. For more details see [ 13 ].”
Cabling and transverse simplicity (2003, methodology): “The overall strategy is not much different from the strategy used in [EH3] and [ EH4 ] to classify and analyze tight contact structures on Seifert fibered spaces over S2 with three singular”
Invariants of Legendrian Knots and Coherent Orientations (2001, background): “knots to detect overtwisted structures and to construct and distinguish tight ones (see [9, 11 , 15, 17], for example).”
Strongly fillable contact 3-manifolds without Stein fillings (2005, background): “Since Legendrian surgery preserves weak fillability by [ 6, Theorem 2.3 ], (−�(2,3,6n + 5),�0) is also weakly fillable.”
Lectures on open book decompositions and contact structures (2004, unknown): “Lemma 5.14 (Etnyre and Honda 2002, [16]; Gay 2002, [19]).”
Ozsváth-Szabó invariants and tight contact three-manifolds, II (2004, background): “ar X iv :m at h/ 05 05 49 3v 2 [ m at AMS Classification 57R17; 57R57 Keywords Ozsváth–Szabó invariants, L–spaces, taut foliations, transverse foliations, transverse contact structures, tight contact structures, planar contact structures”
On symplectic cobordisms (2001, background): “(Note, however, that there are many tight contact structures without such fillings due to Eliashberg [10], Ding-Geiges [5], and Etnyre-Honda [13].)”
Ozsvth-Szab invariants and tight contact 3-manifolds, III (2007, background): “(Tight contact structures on small Seifert fibered 3-manifolds with e0 = −1,−2 have been classified [14, 44], but the classification for e0 = −1,−2 is expected to be considerably harder, due to the presence of nonfillable structures [11, 22] as well as manifolds with no tight contact structures [10,”