(~2,w2lr: 2 ) once ~1 and 1:2 are diffeomorphic, that is, the genera g(~I) and g(~2) are equal. 5 can be checked from the topology of the situation. In the Lagrangian case, on the other hand, wiL = 0 holds, so the topology of L already determines its neighborhood, as the following exercise shows. 2. 7. Show that for L 2 c X 4 Lagrangian we have [L] 2 = -x(L). ) In conclusion, two orientable Lagrangian 2-manifolds in a symplectic 4-manifold admit symplectomorphic neighborhoods if and only if the genera of the surfaces are equal.

Right-handed trefoil knot (e) Prove that ( +5)-surgery on the right-handed trefoil knot is a lens space. ) {f) Show that r-surgery on the right-handed trefoil knot gives the Seifert r~ 6 ). Use this fact to reprove (c) above. fibered manifold M( - ~' Determine the Seifert invariants of the result of (+6)- and (+ 7)-surgeries on the trefoil knot. , - s;(rc2,2n+l)) is diffeomorphic toM(-~' 2n~l'-r- 4~_ 2 ), cf. ) Another family of 3-manifolds is provided by the Brieskorn spheres I:(p, q, r) (p, q, r EN).

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