Quasifibrations (Q1815272)

The authors introduce the notion of ``quasi-fibration''. They show that a quasifibration is either a spread or a maximal partial spread. (If a spread is considered to be a maximal partial spread, a quasifibration can be said to be a maximal partial spread.) The (maximal) partial spreads are defined in terms of vector spaces over possibly infinite fields. Much of the theory of translation planes (spreads), translation nets (partial spreads), and net replacement was developed for the finite case. A finite field is an algebraic extension of a prime field. Much of this works as well for infinite fields which are algebraic extensions of certain subfields. The authors use this idea to construct quasifibrations and to develop a theory of quasifibrations.