On Snake cones, Alternating cones and related constructions
Katsuya Eda, Umed H. Karimov, Du\v{s}an Repov\v{s}, Andreas Zastrow

TL;DR
This paper explores the homotopy equivalences among various cone constructions over the circle, introduces new related constructions, and analyzes their homotopical properties, including the second homology group of a Hawaiian tori wedge.
Contribution
It establishes homotopy equivalences between Snake and alternating cones over the circle and introduces new constructions with detailed homotopical analysis.
Findings
Snake cone over a square is homotopy equivalent to the alternating cone.
Introduces and investigates properties of CSC(-) and CAC(-) constructions.
Explicitly describes the second homology group of the Hawaiian tori wedge.
Abstract
We show that the Snake on a square is homotopy equivalent to the space which was investigated in the previous work by Eda, Karimov and Repov\vs. We also introduce related constructions and and investigate homotopical differences between these four constructions. Finally, we explicitly describe the second homology group of the Hawaiian tori wedge.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis
