## $$PD_3$$-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.

: Primary 57P10.

This paper is available as a pdf (348kB) file. It is also on the arXiv: arxiv.org/abs/2006.08057.

 Thursday, August 20, 2020