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Transactions of the American Mathematical Society

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Cellular automorphisms and self-duality


Authors: Lowell Abrams and Daniel Slilaty
Journal: Trans. Amer. Math. Soc. 367 (2015), 7695-7773
MSC (2010): Primary 05-xx; Secondary 57-xx
DOI: https://doi.org/10.1090/tran/6258
Published electronically: May 20, 2015
MathSciNet review: 3391898
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Abstract: We catalog up to a type of reducibility all cellular automorphisms of the sphere, projective plane, torus, Klein bottle, and three-crosscaps (Dyck's) surface. We also show how one can obtain all self-dual embeddings in a surface $ S$ given a catalog of all irreducible cellular automorphisms in $ S$.


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Additional Information

Lowell Abrams
Affiliation: Department of Mathematics, The George Washington University, Washington, DC 20052
Email: labrams@gwu.edu

Daniel Slilaty
Affiliation: Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435
Email: daniel.slilaty@wright.edu

DOI: https://doi.org/10.1090/tran/6258
Received by editor(s): August 31, 2012
Received by editor(s) in revised form: August 5, 2013
Published electronically: May 20, 2015
Additional Notes: Much of the work in this paper was completed during several visits between the two authors which were funded by the Department of Mathematics of The George Washington University and the Department of Mathematics and Statistics of Wright State University
Dedicated: Dedicated to John B. Conway on the occasion of his retirement
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.