Negative Inflation and Stability in Symplectomorphism Groups of Ruled Surfaces
نویسنده
چکیده
As per journal style, when a display equation takes full width of the column, the equation number (label), goes up of the equation. We are following this style in all JSG articles. So we have ignored the corrections for lines 288-289 and 293-301. Please check whether this is ok. Consider symplectic ruled surfaces M g λ = (Σ g × S 2 , λσ Σg ⊕ σ S 2) such that Σ g has area λ and S 2 has area 1. We show that for k ≥ ≥g/2 the homotopy type of the symplectomorphism groups G g λ of M g λ is constant as λ increases in the interval (k, k + 1], thus generalizing an existent result of Abreu–McDuff for the rational ruled surfaces with g = 0. We also investigate the changes in the groups π * G g λ as λ passes an integer k and show the existence of higher Samelson products in π 4k+2g G g λ that exist only for λ in the range (k, k + 1]. To prove these results we introduce a refinement of the negative inflation technique introduced by Li–Usher.
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