There exists a polyhedron with infinitely many left neighbors

Kołodziejczyk, Danuta

doi:10.1090/S0002-9939-00-05812-3

There exists a polyhedron with infinitely many left neighbors
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Proc. Amer. Math. Soc. 129 (2001), 303-309 Request permission

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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