Homotopy decompositions of polyhedra into products with the second factor S-1

作者：Kolodziejczyk Danuta^*

来源：Topology and Its Applications, 2010, 157(17): 2686-2691.

DOI：10.1016/j.topol.2010.07.019

• Polyhedron
• CW-complex
• ANR
• FANR
• Homotopy type
• Shape
• Direct factor
• Shape factor
• Nilpotent group

As the main results of this paper we prove that for every polyhedron P with abelian or torsion-free nilpotent fundamental group there are only finitely many different homotopy types of X-i such that X-i x S-1 similar or equal to P. The same holds for any finite K(G, 1) with nilpotent fundamental group in place of S-1. The problem, if there exists a polyhedron with infinitely many direct factors of different homotopy types (K. Borsuk, 1970) [2] is still unsolved, even if we assume the second factor to be S-1.

• 出版日期2010-11-1