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Symmetric periodic orbits and uniruled real Liouville domains
Frauenfelder, U.,van Koert, O. Springer Science + Business Media 2016 Chinese annals of mathematics. Ser. B Vol.37 No.4
<P>A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.</P>
Brieskorn manifolds in contact topology
Kwon, Myeonggi,van Koert, Otto Oxford University Press 2016 The bulletin of the London Mathematical Society Vol.48 No.2
<P>In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving exotic contact structures, invariants and orderability. The main tool for the required computations is a version of the Morse-Bott spectral sequence. We provide a proof for the particular version that is useful for us.</P>
Non-fillable invariant contact structures on principal circle bundles and left-handed twists
Chiang, R.,Ding, F.,van Koert, O. WORLD SCIENTIFIC PUBLISHING 2016 International Journal of Mathematics Vol.27 No.3
<P>We define symplectic fractional twists, which subsume Dehn twists and fibered twists and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show that left-handed fractional twists often give rise to 'algebraically overtwisted' contact manifolds, a certain class of non-fillable contact manifolds.</P>
Brieskorn manifolds, positive Sasakian geometry, and contact topology
Boyer, Charles P.,Macarini, Leonardo,van Koert, Otto De Gruyter 2016 Forum mathematicum Vol.28 No.5
<P><B>Abstract</B></P><P>Using[FORMULA OMISSION]-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn–Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various manifolds, including in dimension 5 the<I>k</I>-fold connected sums of[FORMULA OMISSION]and certain rational homology spheres. We then apply our result to show that on these manifolds the moduli space of classes of positive Sasakian structures has infinitely many components. We also apply our results to give lower bounds on the number of components of the moduli space of Sasaki–Einstein metrics on certain homotopy spheres. Finally, a new family of Sasaki–Einstein metrics of real dimension 20 on[FORMULA OMISSION]is exhibited.</P>