\(PD_3\)-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 \(PD_3\)-pairs with aspherical boundary components. This is further extended to pairs \((P,\partial{P})\) which also have spherical boundary components and with \(c.d.\pi_1(P)\leq2\).

Keywords: Algebraic Loop Theorem, free factor, \(PD_3\)-pair, peripheral system.

AMS Subject Classification: Primary 57P10.