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Construction of minimal non-invertible skew-product maps on 2-manifolds


Authors: Jakub Šotola and Sergei Trofimchuk
Journal: Proc. Amer. Math. Soc. 144 (2016), 723-732
MSC (2010): Primary 37B05; Secondary 37E99, 54H20
DOI: https://doi.org/10.1090/proc12749
Published electronically: August 11, 2015
MathSciNet review: 3430848
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Abstract: Applying the Hric-Jäger blow up technique, we give an affirmative answer to the question about the existence of non-invertible minimal circle-fibered self-maps of the Klein bottle. In addition, we present a simpler construction of a non-invertible minimal self-map of two-dimensional torus.


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Additional Information

Jakub Šotola
Affiliation: Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01, Opava, Czech Republic
Email: Jakub.Sotola@math.slu.cz

Sergei Trofimchuk
Affiliation: Instituto de Matemática y Fisica, Universidad de Talca, Casilla 747, Talca, Chile
Email: trofimch@inst-mat.utalca.cl

DOI: https://doi.org/10.1090/proc12749
Received by editor(s): July 16, 2014
Received by editor(s) in revised form: January 29, 2015
Published electronically: August 11, 2015
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

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