Glasnik Matematicki, Vol. 48, No. 1 (2013), 115-135.

ON SNAKE CONES, ALTERNATING CONES AND RELATED CONSTRUCTIONS

Katsuya Eda, Umed H. Karimov, Dušan Repovš and Andreas Zastrow

School of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
e-mail: eda@logic.info.waseda.ac.jp

Institute of Mathematics, Academy of Sciences of Tajikistan, Ul. Ainy 299A, Dushanbe 734063, Tajikistan
e-mail: umedkarimov@gmail.com

Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, P.O.Box 2964, Ljubljana 1001, Slovenia
e-mail: dusan.repovs@guest.arnes.si

Institute of Mathematics, Gdansk University, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
e-mail: zastrow@mat.ug.edu.pl


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.

2010 Mathematics Subject Classification.   54F15, 55N10, 54G20, 55Q52.

Key words and phrases.   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.


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DOI: 10.3336/gm.48.1.11


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