$P{D}_3$-pairs with compressible boundary

Jonathan A. Hillman

Abstract

We extend work of Turaev and Bleile to relax the ${\pi }_1$-injectivity hypothesis in the characterization of the fundamental triples of $P{D}_3$-pairs with aspherical boundary components. This is further extended to pairs $(P,\partial P)$ which also have spherical boundary components and with $c.d.{\pi }_1(P)\le 2$.

Keywords: Algebraic Loop Theorem, free factor, $P{D}_3$-pair, peripheral system.

AMS Subject Classification: Primary 57P10.