On the Gabai-Eliashberg-Thurston theorem (Q1884761)

The authors give a new proof of the Gabai-Eliashberg-Thurston theorem (combining a theorem of Gabai with a theorem of Eliashberg and Thurston) that a closed, oriented, connected, irreducible 3-manifold with nonvanishing second homology carries a universally tight contact structure. The method is built on the convex surfaces theory of Giroux, extended by Kanda, and further developed by the authors. Along the proof of the above theorem, the authors prove a gluing theorem along closed surfaces \(\Sigma\) satisfying a certain extremal condition and provide a good understanding of universally tight contact structures on \(\Sigma\times [0,1]\).