Glasnik matematički, Vol. 48 No. 1, 2013.
Original scientific paper
https://doi.org/10.3336/gm.48.1.11
On Snake cones, alternating cones and related constructions
Katsuya Eda
; School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
Umed H. Karimov
; Institute of Mathematics, Academy of Sciences of Tajikistan, Ul. Ainy 299A, Dushanbe 734063, Tajikistan
Dušan Repovš
orcid.org/0000-0002-6643-1271
; Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, P.O.Box 2964, Ljubljana 1001, Slovenia
Andreas Zastrow
; Institute of Mathematics, Gdansk University, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
Abstract
We show that the Snake on a square SC(S1) is homotopy equivalent to the space AC(S1) which was investigated in the previous work by Eda, Karimov and Repovš. We also introduce related constructions CSC( - ) and CAC( - ) and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.
Keywords
Noncontractible compactum; weak homotopy equivalence; trivial shape; Peano continuum; topologist sine curve; snake on a square; collapsed snake cone; collapsed alternating cone; asphericity; Hawaiian earring; Hawaiian tori
Hrčak ID:
103351
URI
Publication date:
4.6.2013.
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