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On contractible polyhedra that are not simply contractible


Authors: Umed H. Karimov and Dusan Repovs
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Journal: Proc. Amer. Math. Soc. 132 (2004), 2159-2162
MSC (2000): Primary 55M15; Secondary 54G20
DOI: https://doi.org/10.1090/S0002-9939-04-07241-7
Published electronically: February 12, 2004
MathSciNet review: 2053990
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Abstract: In answer to a question of Michael, Dydak, Segal and Spiez have constructed a contractible polyhedron that is not strictly contractible. In the present note we prove a related result; by using alternative methods we show that there exist contractible polyhedra that are not simply (hence not strictly) contractible.


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Additional Information

Umed H. Karimov
Affiliation: Institute of Mathematics, Academy of Sciences Tajikistan, Ul. Ainy $299^{A}$, Dushanbe, Tajikistan 734063
Email: umed-karimov@mail.ru

Dusan Repovs
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001
Email: dusan.repovs@uni-lj.si

DOI: https://doi.org/10.1090/S0002-9939-04-07241-7
Keywords: Absolute retract, polyhedron, strong retract, strict contractibility, simple contractibility, collapsibility
Received by editor(s): April 30, 2002
Received by editor(s) in revised form: January 28, 2003, and April 4, 2003
Published electronically: February 12, 2004
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society