Real tight contact structures on lens spaces and surface singularities

S Onaran, F Ozturk�- Journal of Topology and Analysis, 2023 - World Scientific
S Onaran, F Ozturk
Journal of Topology and Analysis, 2023World Scientific
We give a partial classification for the real tight contact structures on solid tori up to
equivariant contact isotopy and apply the results to the classification of real tight structures
on S 3 and real lens spaces L (p,�1). We prove that there is a unique real tight S 3 and ℝ P
3. We show that there is at most one real tight L (p,�1) with respect to one of its two possible
real structures. With respect to the other we give lower and upper bounds for the count. To
establish lower bounds we explicitly construct real tight manifolds through equivariant�…
We give a partial classification for the real tight contact structures on solid tori up to equivariant contact isotopy and apply the results to the classification of real tight structures on and real lens spaces . We prove that there is a unique real tight and . We show that there is at most one real tight with respect to one of its two possible real structures. With respect to the other we give lower and upper bounds for the count. To establish lower bounds we explicitly construct real tight manifolds through equivariant contact surgery, real open book decompositions and isolated real algebraic surface singularities. As a by-product we observe the existence of an invariant torus in an which cannot be made convex equivariantly.
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