Symplectic spreads and symplectically paired spreads


Abstract


If 𝜋 is a finite symplectic translation plane, it is shown that any affine homology group is cyclic and has order dividing the order of the kernel homology group. This criterion provides a means to ensure that a given spread is not symplectic. Furthermore, a variety of symplectically paired André spreads are constructed.

DOI Code: 10.1285/i15900932v26n2p119

Keywords: Translation planes; Symplectic spreads; Affine homologies; Symplectically paired spreads

Classification: 51E23; 51A40

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