$PD_3$-pairs with compressible boundary
Geometric Topology
2026-05-15 v7 Algebraic Topology
Abstract
We extend work of Turaev and Bleile to relax the -injectivity hypothesis in the characterization of the fundamental triples of -pairs with aspherical boundary components. This is further extended to pairs which also have spherical boundary components and with .
Cite
@article{arxiv.2006.08057,
title = {$PD_3$-pairs with compressible boundary},
author = {Jonathan A. Hillman},
journal= {arXiv preprint arXiv:2006.08057},
year = {2026}
}
Comments
v2:"geometric" homomorphisms identified, Theorem 7 rewritten. v3: estimates for free group factor. v4: rewritten. v5: \S5 rewritten, to bring forward the difference between the Algebraic and Topological Loop Theorems v6:new \s4 split off \S3 and new Corollary 11 split off Theorem 9. v7. \S4-\S6 rewritten, and examples illustrating independence of key hypotheses added