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Symplectic spreads and symplectically paired spreads. (English) Zbl 1118.51010

If \(\pi\) is a 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.

MSC:

51E23 Spreads and packing problems in finite geometry
51A40 Translation planes and spreads in linear incidence geometry
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