Nielsen classes of orientation reversing homeomorphisms and complementary domains of plane separating invariant continua |
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Authors: | J.P. Boroński |
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Affiliation: | a Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland b Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA |
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Abstract: | Let h be an orientation reversing planar homeomorphism and X be an invariant plane separating continuum. We show that there is a natural linear order on the invariant components of R2?X that resemble the one found in connected unions of circles invariant under the reflection r(x,y)=(−x,y). The main result relates to the Nielsen fixed point theory and work of Krystyna Kuperberg on fixed points of planar homeomorphisms in invariant continua. |
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Keywords: | 37E30 54F15 55M20 |
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