Geodesic
Polyhedra with finite fundamental group dominate finitely many different homotopy types
Danuta Kołodziejczyk1
1Faculty of Mathematics and Informational Sciences Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland
Fundamenta Mathematicae, Tome 180 (2003) no. 1, pp. 1-9
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In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.
DOI : 10.4064/fm180-1-1
Keywords: borsuk asked does every polyhedron dominate only finitely many different shapes question notion shape replaced notion homotopy type showed earlier answer borsuk question however previous paper proved every simply connected polyhedron dominates only finitely many different homotopy types equivalently shapes here prove polyhedra finite fundamental group

Danuta Kołodziejczyk  1

1 Faculty of Mathematics and Informational Sciences Warsaw University of Technology Pl. Politechniki 1 00-661 Warszawa, Poland 
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 dominate finitely many different homotopy types},
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 dominate finitely many different homotopy types
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 dominate finitely many different homotopy types
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Danuta Kołodziejczyk. Polyhedra with finite fundamental group 
 dominate finitely many different homotopy types. Fundamenta Mathematicae, Tome 180 (2003) no. 1, pp. 1-9. doi: 10.4064/fm180-1-1

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