This paper is the first of three which will investigate the ring of cobordism classes of closed smooth manifolds with a symplectic structure on their stable normal bundle. The method of computation is the Adams spectral sequence. In this paper, [italic]E2 us computed as an algebra by the May spectral sequence. The [italic]d2 differentials in the Adams spectral sequence are then found by Landweber-Novikov and matric Massey product methods. Algebra generators of [italic]E3 are then determined.
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