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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

On minimal Poincaré 4-complexes

Alberto CAVICCHIOLI,Friedrich HEGENBARTH,Duşan REPOVŞ

Pages
535–557
DOI
—

Abstract

We consider 2 types of minimal Poincaré 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 by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.

Özet

We consider 2 types of minimal Poincaré 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 by Hillman. The second type of minimal Poincaré 4-complexes was introduced by Hambleton, Kreck, and Teichner. It is not based on an order relation. In the present paper we study existence and uniqueness questions.

Keywords: Poincaré 4-complex, equivariant intersection form, degree 1-map, k-invariant, homotopy type, obstruction theory, homology with local coefficients, Whitehead's quadratic functor, Whitehead's exact sequence