Atomic Properties of the Hawaiian Earring Group for HNN Extensions |
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Authors: | Jun Nakamura |
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Institution: | 1. Department of Mathematics , Waseda University , Tokyo , Japan cardioid@toki.waseda.jp |
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Abstract: | In 2011, while investigating fundamental groups of wild spaces, K.Eda 7
Eda , K. ( 2011 ). Atomic property of the fundamental groups of the Hawaiian earring and wild locally path-connected spaces . Jour. Math. Soc. Japan 63 ( 3 ): 769 – 787 .Crossref], Web of Science ®] , Google Scholar]] showed that the fundamental group of the Hawaiian earring (the Hawaiian earring group, in short) ![/></span> has the property that for any homomorphism <i>h</i> from it to a free product <i>A</i>*<i>B</i>, there exists a natural number <i>N</i> such that <span class=](/na101/home/literatum/publisher/tandf/journals/content/lagb20/2015/lagb20.v043.i10/00927872.2014.939273/20150706/images/medium/lagb_a_939273_o_ilf0001.gif) ![/></span> is contained in a conjugate subgroup to <i>A</i> or <i>B</i>. In the present article, we prove a corresponding property for certain HNN extensions and amalgamated free products. This allows us to show that some one-relator groups, including Baumslag–Solitar groups, are <i>n</i>-slender.</td>
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Keywords: | Baumslag-Solitar groups HNN extension Hawaiian earring Infinitary words N-slender |
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