Algebraic & Geometric Topology

An indecomposable $PD_3$–complex : II

Jonathan A Hillman

Full-text: Open access


We show that there are two homotopy types of PD3–complexes with fundamental group S3Z2ZS3, and give explicit constructions for each, which differ only in the attachment of the top cell.

Article information

Algebr. Geom. Topol., Volume 4, Number 2 (2004), 1103-1109.

Received: 4 August 2004
Accepted: 16 November 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57P10: Poincaré duality spaces
Secondary: 55M05: Duality

indecomposable Poincaré duality $PD_3$–complex


Hillman, Jonathan A. An indecomposable $PD_3$–complex : II. Algebr. Geom. Topol. 4 (2004), no. 2, 1103--1109. doi:10.2140/agt.2004.4.1103.

Export citation


  • Handel, D. On products in the cohomology of the dihedral groups, Tôhoku Math. J. 45 (1993), 13-42.
  • Hillman, J.A. On 3-dimensional Poincaré duality complexes and 2-knot groups, Math. Proc. Cambridge Phil. Soc. 114 (1993), 215-218.
  • Hillman, J.A. An indecomposable $PD_3$-complex whose group has infinitely many ends, Math. Proc. Cambridge Phil. Soc., to appear (2005).
  • Swan, R.G. Periodic resolutions for finite groups. Ann. of Math. 72 (1960), 267-291.
  • Turaev, V.G. Three-dimensional Poincaré complexes: homotopy classification and splitting. Math. USSR-Sb. 67 (1990), 261-282. MR1015042 (91c:57031) Turaev, V. G. Three-dimensional Poincaré complexes: homotopy classification and splitting. (Russian) Mat. Sb. 180 (1989), no. 6, 809–830.
  • Wall, C.T.C. Poincaré complexes: I. Ann. of Math. 86 (1967), 213-245.
  • Wall, C.T.C. Poincaré duality in dimension 3, in Proceedings of the Casson Fest (Arkansas and Texas 2003) (edited by C.McA.Gordon and Y.Rieck), Geom. Topol. Monogr. 7 (2004), 1-26.