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There exists a polyhedron with infinitely many left neighbors

Author(s): Danuta Kolodziejczyk
Journal: Proc. Amer. Math. Soc. 129 (2001), 303-309.
MSC (2000): Primary 55P55, 55P15
Posted: August 30, 2000
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Abstract:

We show that there exists a finite polyhedron $P$ homotopy dominating infinitely many finite polyhedra $K_i$ of different homotopy types such that there isn't any homotopy type between $P$ and $K_i$. This answers negatively the question raised by K. Borsuk in 1975: Does every FANR have only finitely many left neighbors?

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Additional Information:

Danuta Kolodziejczyk
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warsaw, Poland - Address for correspondence: ul. Jasna 8/18, 00-013 Warsaw, Poland
Address at time of publication: Department of Mathematics and Informational Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warsaw, Poland
Email: dkolodz@mimuw.edu.pl

DOI: 10.1090/S0002-9939-00-05812-3
PII: S 0002-9939(00)05812-3
Keywords: Shape, homotopy type, FANR, polyhedron, shape domination, homotopy domination, left neighbor
Received by editor(s): February 28, 1999
Posted: August 30, 2000
Additional Notes: The author would like to thank the Institute of Mathematics of the Polish Academy of Sciences for its support while this work was done.
Communicated by: Ralph Cohen
Copyright of article: Copyright 2000, American Mathematical Society

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