Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On contractible polyhedra that are not simply contractible

Authors: Umed H. Karimov and Dusan Repovs
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2159-2162
MSC (2000): Primary 55M15; Secondary 54G20
Published electronically: February 12, 2004
MathSciNet review: 2053990
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] W. H. Beckman, A certain class of nonaspherical $2$-complexes, J. Pure Appl. Algebra 16 (1980), 243-244. MR 81d:57003
  • [2] J. Dydak, J. Segal, and S. Spiez, On questions of strict contractibility, Topology Appl. 120 (2002), 67-75. MR 2003c:55010
  • [3] G. Higman, A finitely generated infinite simple group, J. London Math. Soc. 26 (1951), 61-64. MR 12:390c
  • [4] C. Hog-Angeloni and W. Metzler, Geometric aspects of two-dimensional complexes, Two-dimensional Homotopy and Combinatorial Group Theory, London Math. Soc. Lecture Notes 197, Cambridge University Press, Cambridge, 1993, pp. 1-50.
  • [5] U. H. Karimov and D. Repovs, On suspensions of noncontractible compacta of trivial shape, Proc. Amer. Math. Soc. 127 (1999), 627-632. MR 99c:54023
  • [6] E. Michael, Closed retracts and perfect retracts, Topology Appl. 121 (2002), 451-468. MR 2003i:54015
  • [7] H. Seifert and W. Threlfall, A Textbook of Topology, Pure and Appl. Math., vol. 89, Academic Press, New York, 1980. MR 82b:55001
  • [8] E. H. Spanier, Algebraic Topology, Springer-Verlag, New York, 1966; Corrected reprint, 1981. MR 83i:55001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55M15, 54G20

Retrieve articles in all journals with MSC (2000): 55M15, 54G20

Additional Information

Umed H. Karimov
Affiliation: Institute of Mathematics, Academy of Sciences Tajikistan, Ul. Ainy $299^{A}$, Dushanbe, Tajikistan 734063

Dusan Repovs
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001

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

American Mathematical Society