# PD4-complexes with strongly minimal models

@article{Hillman2006PD4complexesWS, title={PD4-complexes with strongly minimal models}, author={J. Hillman}, journal={Topology and its Applications}, year={2006}, volume={153}, pages={2413-2424} }

Abstract Let X be a PD 4 -complex with fundamental group π. We give conditions on the algebraic 2-type of X under which the homotopy type of X is determined by π, w = w 1 ( X ) , the image of [ X ] in H 4 ( π ; Z w ) and the equivariant intersection pairing on π 2 ( X ) . In particular, the homotopy type of an oriented spin 4-manifold with fundamental group a PD 2 -group π is determined by π and this pairing.

#### 12 Citations

Strongly minimal PD4-complexes

- Mathematics
- 2009

Abstract We consider the homotopy types of PD 4 -complexes X with fundamental group π such that c . d . π = 2 and π has one end. Let β = β 2 ( π ; F 2 ) and w = w 1 ( X ) . Our main result is that… Expand

PD4-Complexes and 2-Dimensional Duality Groups

- Mathematics
- 2021

This paper is a synthesis and extension of three earlier papers on PD4-complexes X such that π = π1(X) has one end and c.d.π = 2. The basic notion is that of strongly minimal PD4-complex, one for… Expand

Homotopy self-equivalences of 4-manifolds with PD2 fundamental group

- Mathematics
- 2009

Abstract Based on the approach of Hambleton and Kreck, an explicit description of the group of homotopy classes of homotopy self-equivalences of an orientable 4-manifold is obtained when the… Expand

On minimal Poincaré 4-complexes

- Mathematics
- 2014

We consider 2 types of minimal Poincare 4-complexes. One is defined with respect to the degree 1-map order. This idea was already present in our previous papers, and more systematically studied later… Expand

TOPOLOGICAL 4-MANIFOLDS WITH GEOMETRICALLY TWO-DIMENSIONAL FUNDAMENTAL GROUPS

- Mathematics
- 2008

Closed oriented 4-manifolds with the same geometrically two-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w2-type, equivariant intersection… Expand

Poincare duality complexes in dimension four

- Mathematics
- 2008

We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of Poincare duality complexes of dimension 4. Generalizing Turaev's fundamental triples… Expand

$PD_4$-complexes: constructions, cobordisms and signatures

- Mathematics
- 2016

The oriented topological cobordism group Ω4(P ) of an oriented PD4-complex P is isomorphic to Z⊕ Z. The invariants of an element {f : X → P} ∈ Ω4(P ) are the signature of X and the degree of f . We… Expand

Homotopy classification of $$\textit{PD}_4$$PD4-complexes relative an order relation

- Mathematics
- 2015

We define an order relation among oriented $$\textit{PD}_4$$PD4-complexes. We show that with respect to this relation, two $$\textit{PD}_4$$PD4-complexes over the same complex are homotopy equivalent… Expand

Four-Dimensional Complexes with Fundamental Class

- Mathematics
- 2020

This paper continues the study of 4-dimensional complexes from our previous work Cavicchioli et al. (Homol Homotopy Appl 18(2):267–281, 2016; Mediterr J Math 15(2):61, 2018. … Expand

Homotopy Self-Equivalences of 4-manifolds with Free Fundamental Group

- Mathematics
- Canadian Journal of Mathematics
- 2010

Abstract We calculate the group of homotopy classes of homotopy self-equivalences of 4-manifolds with free fundamental group and obtain a classification of such 4-manifolds up to s-cobordism.

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