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On composants of the bucket handle. (English) Zbl 0759.54017
The class group $${\mathcal Cl}({\mathcal S}_ 2)$$, where $${\mathcal S}_ 2$$ denotes the 2-solenoid, is the group of base point preserving homeomorphisms of $$\mathcal{S}_ 2$$ up to base point preserving isotopy. The class group $${\mathcal Cl}({\mathcal K})$$, where $$\mathcal K$$ denotes the bucket handle continuum, is the group of homeomorphisms of $$\mathcal K$$ up to isotopy. The authors prove that $${\mathcal Cl}({\mathcal S}_ 2)$$ is isomorphic to $$\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z}$$, and that $${\mathcal Cl}({\mathcal K})$$ is isomorphic to $$\mathbb{Z}$$. They also show that if $$C$$ and $$D$$ are composants of $$\mathcal K$$ not containing the end point 0, then there exists an injective continuous map $$\Phi: {\mathcal K}-\{0\}\to {\mathcal K} - \{0\}$$ which maps $$C$$ onto $$D$$.
Reviewer: K.M.Kuperberg

##### MSC:
 54F15 Continua and generalizations 54H20 Topological dynamics (MSC2010)
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