SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES
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We present smooth simply connected closed 4k-dimensional manifolds N := Nπ, for each k β {2, 3, β¦ }, with distinct symplectic deformation equivalence classes [[Οπ]], π = 1, 2. To distinguish [[Οπ]]'s, we used the symplectic π invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that π(N, [[Ο1]]) = β and π(N, [[Ο2]]) < 0.
Abstract
We present smooth simply connected closed 4k-dimensional manifolds N := Nπ, for each k β {2, 3, β¦ }, with distinct symplectic deformation equivalence classes [[Οπ]], π = 1, 2. To distinguish [[Οπ]]'s, we used the symplectic π invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that π(N, [[Ο1]]) = β and π(N, [[Ο2]]) < 0.
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- R. Barlow, "A Simply Connected Surface of General Type with pg = 0", Invent. Math, 79, pp.293~301 (1985)
- F. Catanese, "On the scalar curvature of Einstein manifolds", Math. Research Letters, 4, pp.843~854 (1997)
- κΉμ’ μ, "A simply connected manifold with two symplectic deformation equivalence classes with distinct signs of scalar curvatures", λνμννλ Όλ¬Έμ§, 29(4), pp.549~554 (2014), λνμνν
- "Scalar Curvature Functions of Almost-KΓahler Metrics" (2015)[URL]
- D. McDuff, "Introduction to Symplectic Topology" (1998), Oxford University Press
- C.T. McMullen, "4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations", Math. Res. Lett, 6, pp.681~696 (1999)
- Y. Ruan, "Symplectic topology on algebraic 3-folds", J. Differential Geom, 39, pp.215~227 (1994)
- D. Salamon, "Uniqueness of symplectic structures", Acta Math. Vietnam, 38, pp.123~144 (2013)