|
On contractible polyhedra that are not simply contractible
Author(s):
Umed
H.
Karimov;
Dusan
Repovs
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2159-2162.
MSC (2000):
Primary 55M15;
Secondary 54G20
Posted:
February 12, 2004
MathSciNet review:
2053990
Retrieve article in:
PDF
This article is available free of charge
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:
-
- [1]
- W. H. Beckman, A certain class of nonaspherical
 -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
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:
10.1090/S0002-9939-04-07241-7
PII:
S 0002-9939(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
Posted:
February 12, 2004
Communicated by:
Alan Dow
Copyright of article:
Copyright
2004,
American Mathematical Society
|
