2003/03/23 by Paolo Lisca, P. Lisca, András I. Stipsicz +3
Computer Science · Mathematics · #57R17 #57R57 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:57R17 #msc:57R57 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0303280
7 pages, 4 figures; improved exposition, corrected typos
openalex publication_date 2003/03/23 · arxiv created 2003/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Y(r) be the closed, oriented three-manifold obtained by performing rational r-surgery on the right-handed trefoil knot in the three-sphere. Using contact surgery and the Heegaard Floer contact invariants we construct positive, tight contact structures on Y(r) for every r not equal to 1. This implies, in particular, that the oriented boundaries of the positive E6 and E7 plumbings carry positive, tight contact structures, solving a well-known open problem.