Sewings of closed four-cell complements

This dissertation makes four contributions to the theory of four dimensional sewings. First, two new concepts are introduced and explored extensively; one is shown to lead to a classification of closed four-cell complements which is analogous to the classification of closed n-cell complements (n > 5) by types. Second, we find wide classes of closed four-cell complements for which the 4 identity sewing yields S⁴. Third, we show that suspensions of closed three-cell complements are universal, and we make other investigations into universality. Fourth and last, we adapt five pathological examples from the theory of high dimensional sewings to the case n = 4.